Co-Development of Obesity Risk, Depressive Symptoms, and Relative Pubertal Development

Purpose

This code conducts the data prep and analysis for a within race/ethnicity analysis for depression (CBCL - Depressin Subscale), obesity risk (Waist Circumference to Height Ratio [WC/HT]), and relative pubertal timing (Pubertal Development Scale) in ABCD.

Identifiers

##rm(list = ls()) 
library(psych)

#Load subject and family identifiers
Identifiers <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/abcd-general/abcd_y_lt.csv", header = TRUE, sep = ",", dec = ".")
#View(identifiers)

#print variable names and labels
#print(Identifiers[1,])

#Create key for Identifiers:
Identifiers.varlabels <- Identifiers[1,]

#Remove first row of Identifiers so we are left with only the data:
Identifiers.data <- Identifiers[-1,]

# Rename/recode variables
Identifiers.data$IID  <- Identifiers.data[,"src_subject_id"]
Identifiers.data$FID  <- Identifiers.data[,"rel_family_id"]
Identifiers.data$BID  <- Identifiers.data[,"rel_birth_id"]
#dim(Identifiers.data)

Identifiers.data <- Identifiers.data[order(Identifiers.data$IID,Identifiers.data$FID,Identifiers.data$BID),] 

#View(Identifiers.data)

Baseline.Identifiers<-Identifiers.data[Identifiers.data$eventname=="baseline_year_1_arm_1",]
Y1.Identifiers<-Identifiers.data[Identifiers.data$eventname=="1_year_follow_up_y_arm_1",]
Y2.Identifiers<-Identifiers.data[Identifiers.data$eventname=="2_year_follow_up_y_arm_1",]
Y3.Identifiers<-Identifiers.data[Identifiers.data$eventname=="3_year_follow_up_y_arm_1",]

#print(names(Identifiers.data))
#table(Identifiers.data$eventname)
#summary(Y1.data$interview_age)

# Load demographic data
demo <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/abcd-general/abcd_p_demo.csv", header = TRUE, sep = ",", dec= ".")
# View(identifiers)

# Print variable names and labels
#print(demo[1,])

# Create key for Identifiers:
demo.varlabels <- demo[1,]

# Remove first row of Identifiers so we are left with only the data:
demo.data <- demo[-1,]

# Rename subject ID
demo.data$IID  <- demo.data[,"src_subject_id"]

# Baseline 
Baseline.demo<-demo.data[demo.data$eventname=="baseline_year_1_arm_1",]
colnames(Baseline.demo)[colnames(Baseline.demo) == "demo_sex_v2"] <- "sex"

# Create binary variables for each race/ethnicity
# 1 = White; 2 = Black; 3 = Hispanic; 4 = Asian; 5 = Other
freq_table <- table(Baseline.demo$race_ethnicity)
print(freq_table)

## 
##    1    2    3    4    5 
## 6172 1784 2410  252 1247

# Create binary variables for each race/ethnicity
Baseline.demo$White <- ifelse(Baseline.demo$race_ethnicity == 1, 1, 0)
Baseline.demo$Black <- ifelse(Baseline.demo$race_ethnicity == 2, 1, 0)
Baseline.demo$Hispanic <- ifelse(Baseline.demo$race_ethnicity == 3, 1, 0)
Baseline.demo$Asian <- ifelse(Baseline.demo$race_ethnicity == 4, 1, 0)
Baseline.demo$Other <- ifelse(Baseline.demo$race_ethnicity == 5, 1, 0)

# Frequency Tables for race/ethnicity
freq_White <- table(Baseline.demo$White)
print(freq_White)

## 
##    0    1 
## 5693 6172

freq_Black <- table(Baseline.demo$Black)
print(freq_Black)

## 
##     0     1 
## 10081  1784

freq_Hispanic <- table(Baseline.demo$Hispanic)
print(freq_Hispanic)

## 
##    0    1 
## 9455 2410

freq_Asian <- table(Baseline.demo$Asian)
print(freq_Asian)

## 
##     0     1 
## 11613   252

freq_Other <- table(Baseline.demo$Other)
print(freq_Other)

## 
##     0     1 
## 10618  1247

# Subset dataset for White, Black, Hispanic
Baseline.demo <- subset(Baseline.demo, White == 1 | Black == 1 | Hispanic == 1)

# Create indicator var for subset analyses
Baseline.demo$race3 <- ifelse(Baseline.demo$White == 1, 1, 
                          ifelse(Baseline.demo$Black == 1, 2, 
                          ifelse(Baseline.demo$Hispanic == 1, 3, NA)))
freq_race3 <- table(Baseline.demo$race3)
#print(freq_race3)

# Subset so later data sets are smaller
Baseline.demo <- Baseline.demo[, c("IID", "sex", "race_ethnicity", "White", 
                                   "Black", "Hispanic", "Asian", "Other", "race3", 
                                   "demo_prnt_ed_v2_2yr_l", # Respondent 
                                   "demo_prtnr_ed_v2_2yr_l", # Partner
                                   "demo_comb_income_v2",
                                   "demo_prnt_age_v2")]

Internalizing - Depression Subscale (int)

#Load cbcl data
cbcl <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/mental-health/mh_p_cbcl.csv", header = TRUE, sep = ",", dec = ".")

#View(cbcl)
describe(cbcl$cbcl_scr_syn_withdep_r) #Internalizing CBCL Syndrome Scale (raw score)

##    vars     n mean   sd median trimmed mad min max range skew kurtosis   se
## X1    1 48727 1.24 1.96      0    0.81   0   0  16    16 2.32     6.61 0.01

summary(cbcl$cbcl_scr_syn_withdep_r)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   0.000   0.000   1.244   2.000  16.000      10

#Create key for Identifiers:
cbcl.varlabels <- cbcl[1,]

#Remove first row of Identifiers so we are left with only the data:
cbcl.data <- cbcl[-1,]

#Rename subject ID
cbcl.data$IID  <- cbcl.data[,"src_subject_id"]

#Create 0, 1, 2,3 assessment data sets
Baseline.cbcl<-cbcl.data[cbcl.data$eventname=="baseline_year_1_arm_1",]
Y1.cbcl<-cbcl.data[cbcl.data$eventname=="1_year_follow_up_y_arm_1",]
Y2.cbcl<-cbcl.data[cbcl.data$eventname=="2_year_follow_up_y_arm_1",]
Y3.cbcl<-cbcl.data[cbcl.data$eventname=="3_year_follow_up_y_arm_1",]

###############################################################################
################################ Baseline (10.5)###############################
###############################################################################

# Merge Baseline.cbcl with Baseline.Identifiers based on IID to get age
Merged.Baseline_cbcl_identifiers <- merge(Baseline.cbcl, Baseline.Identifiers, by = "IID")

# Then, merge Merged.Baseline_cbcl_identifiers with baseline.demo based on IID to get sex variable
Merged.Baseline_ID_cbcl <- merge(Merged.Baseline_cbcl_identifiers, Baseline.demo, by = "IID")

############### Regress age out of depression score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# Rename variables for code below
colnames(Merged.Baseline_ID_cbcl)[colnames(Merged.Baseline_ID_cbcl) == "interview_age"] <- "age"
colnames(Merged.Baseline_ID_cbcl)[colnames(Merged.Baseline_ID_cbcl) == "cbcl_scr_syn_withdep_r"] <- "int" 

# Subset the data
int_raw <- Merged.Baseline_ID_cbcl[, c("IID", "age", "sex", "int" )]

# Make data set for boys and girls
boys_data <- int_raw[int_raw$sex == 1, ]
girls_data <- int_raw[int_raw$sex == 2, ]

#################### Regress internalizing scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on int and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
boys_data$intt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress int scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on int and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
girls_data$intt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine intt variables and create a new combined intt column
merged_data <- merged_data %>%
  mutate(intt = coalesce(intt.boys, intt.girls))

# Display the merged data with combined intt variable
# print(merged_data)

# Subset to only IDD and intt score
merged_data <- merged_data[, c("IID", "intt")]

# Merge with raw int data
merged_int <- merge(int_raw, merged_data, by = "IID", all = TRUE)
# print(merged_int)

# Rename variables to keep in each assessment data set
library(data.table)

## 
## Attaching package: 'data.table'

## The following objects are masked from 'package:dplyr':
## 
##     between, first, last

variables_to_keep_Baseline <- c("IID","int","intt", "age")

# Convert the data frame to a data.table
setDT(merged_int)

# Subset the data table and create a new data table
subset_data <- merged_int[, ..variables_to_keep_Baseline]

# Rename the columns by appending "_Baseline"
colnames(subset_data) <- paste0(colnames(subset_data), "_Baseline")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Baseline"] <- "IID"

# rename data set for merge
int_Baseline <- subset_data

###############################################################################
################################ Year 1 (11.5) ################################
###############################################################################

# Merge Baseline.cbcl with Baseline.Identifiers based on IID to get age
Merged.Y1_cbcl_identifiers <- merge(Y1.cbcl, Y1.Identifiers, by = "IID")

# Then, merge Merged.Y1_cbcl_identifiers with baseline.demo based on IID to get sex variable
Merged.Y1_ID_cbcl <- merge(Merged.Y1_cbcl_identifiers, Baseline.demo, by = "IID")

############### Regress age out of BMI score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

# Rename variables for code below
colnames(Merged.Y1_ID_cbcl)[colnames(Merged.Y1_ID_cbcl) == "interview_age"] <- "age"
colnames(Merged.Y1_ID_cbcl)[colnames(Merged.Y1_ID_cbcl) == "cbcl_scr_syn_withdep_r"] <- "int"

# Subset the data
int_raw <- Merged.Y1_ID_cbcl[, c("IID", "age", "sex", "int" )]

# Make data set for boys and girls
boys_data <- int_raw[int_raw$sex == 1, ]
girls_data <- int_raw[int_raw$sex == 2, ]

#################### Regress internalizing scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on int and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
boys_data$intt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress int scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on int and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
girls_data$intt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine intt variables and create a new combined intt column
merged_data <- merged_data %>%
  mutate(intt = coalesce(intt.boys, intt.girls))

# Display the merged data with combined intt variable
# print(merged_data)

# Subset to only IDD and intt score
merged_data <- merged_data[, c("IID", "intt")]

# Merge with raw int data
merged_int <- merge(int_raw, merged_data, by = "IID", all = TRUE)
# print(merged_int)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y1 <- c("IID","int","intt", "age")

# Convert the data frame to a data.table
setDT(merged_int)

# Subset the data table and create a new data table
subset_data <- merged_int[, ..variables_to_keep_Y1]

# Rename the columns by appending "_Y1"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y1")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y1"] <- "IID"

# rename data set for merge
int_Y1 <- subset_data

###############################################################################
################################ Year 2 (12.5) ################################
###############################################################################

# Merge Baseline.cbcl with Baseline.Identifiers based on IID to get age
Merged.Y2_cbcl_identifiers <- merge(Y2.cbcl, Y2.Identifiers, by = "IID")

# Then, merge Merged.Y2_cbcl_identifiers with baseline.demo based on IID to get sex variable
Merged.Y2_ID_cbcl <- merge(Merged.Y2_cbcl_identifiers, Baseline.demo, by = "IID")

############### Regress age out of BMI score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

# Rename variables for code below
colnames(Merged.Y2_ID_cbcl)[colnames(Merged.Y2_ID_cbcl) == "interview_age"] <- "age"
colnames(Merged.Y2_ID_cbcl)[colnames(Merged.Y2_ID_cbcl) == "cbcl_scr_syn_withdep_r"] <- "int"

# Subset the data
int_raw <- Merged.Y2_ID_cbcl[, c("IID", "age", "sex", "int" )]

# Make data set for boys and girls
boys_data <- int_raw[int_raw$sex == 1, ]
girls_data <- int_raw[int_raw$sex == 2, ]

#################### Regress internalizing scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on int and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
boys_data$intt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress int scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on int and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
girls_data$intt <- residuals

# Display the modified data table with residuals
#print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine intt variables and create a new combined intt column
merged_data <- merged_data %>%
  mutate(intt = coalesce(intt.boys, intt.girls))

# Display the merged data with combined intt variable
# print(merged_data)

# Subset to only IDD and intt score
merged_data <- merged_data[, c("IID", "intt")]

# Merge with raw int data
merged_int <- merge(int_raw, merged_data, by = "IID", all = TRUE)
# print(merged_int)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y2 <- c("IID","int","intt", "age")

# Convert the data frame to a data.table
setDT(merged_int)

# Subset the data table and create a new data table
subset_data <- merged_int[, ..variables_to_keep_Y2]

# Rename the columns by appending "_Y2"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y2")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y2"] <- "IID"

# rename data set for merge
int_Y2 <- subset_data

###############################################################################
################################ Year 3 (13.5) ################################
###############################################################################

# Merge Baseline.cbcl with Baseline.Identifiers based on IID to get age
Merged.Y3_cbcl_identifiers <- merge(Y3.cbcl, Y3.Identifiers, by = "IID")

# Then, merge Merged.Y3_cbcl_identifiers with baseline.demo based on IID to get sex variable
Merged.Y3_ID_cbcl <- merge(Merged.Y3_cbcl_identifiers, Baseline.demo, by = "IID")

############### Regress age out of BMI score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

# Rename variables for code below
colnames(Merged.Y3_ID_cbcl)[colnames(Merged.Y3_ID_cbcl) == "interview_age"] <- "age"
colnames(Merged.Y3_ID_cbcl)[colnames(Merged.Y3_ID_cbcl) == "cbcl_scr_syn_withdep_r"] <- "int"

# Subset the data
int_raw <- Merged.Y3_ID_cbcl[, c("IID", "age", "sex", "int" )]

# Make data set for boys and girls
boys_data <- int_raw[int_raw$sex == 1, ]
girls_data <- int_raw[int_raw$sex == 2, ]

#################### Regress internalizing scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on int and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = boys_data)
#summary(model)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
boys_data$intt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress int scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on int and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$int), ]

# Fit the linear regression model
model <- lm(int ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into intt var
girls_data$intt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine intt variables and create a new combined intt column
merged_data <- merged_data %>%
  mutate(intt = coalesce(intt.boys, intt.girls))

# Display the merged data with combined intt variable
# print(merged_data)

# Subset to only IDD and intt score
merged_data <- merged_data[, c("IID", "intt")]

# Merge with raw int data
merged_int <- merge(int_raw, merged_data, by = "IID", all = TRUE)
# print(merged_int)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y3 <- c("IID","int","intt", "age")

# Convert the data frame to a data.table
setDT(merged_int)

# Subset the data table and create a new data table
subset_data <- merged_int[, ..variables_to_keep_Y3]

# Rename the columns by appending "_Y3"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y3")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y3"] <- "IID"

# rename data set for merge
int_Y3 <- subset_data

############### Merge all internalizing data sets together  ####################

# Merge all int data sets together
library(data.table)

# List of datasets to merge
int_datasets <- list(int_Baseline, int_Y1, int_Y2, int_Y3)

# Merge all data.tables using full outer join based on IID
int_merged_data <- Reduce(function(x, y) merge(x, y, by = "IID", all = TRUE), int_datasets)

Descriptives (int)

# Internalizing Descriptive Statistics
library(psych)

# Select the variables you want to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3")

# Convert data.table to data frame
data_frame <- as.data.frame(int_merged_data)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##               vars     n   mean   sd median trimmed   mad    min    max range
## age_Baseline     1 10360 118.97 7.49 119.00  118.87 10.38 107.00 133.00 26.00
## int_Baseline     2 10358   1.03 1.70   0.00    0.64  0.00   0.00  15.00 15.00
## intt_Baseline    3 10355   0.00 1.70  -0.91   -0.37  0.34  -1.16  13.91 15.08
## age_Y1           4  9784 131.08 7.72 131.00  130.99 10.38 117.00 149.00 32.00
## int_Y1           5  9783   1.11 1.78   0.00    0.71  0.00   0.00  14.00 14.00
## intt_Y1          6  9780   0.00 1.77  -0.99   -0.38  0.36  -1.30  12.91 14.21
## age_Y2           7  9523 144.28 8.01 144.00  144.18 10.38 127.00 168.00 41.00
## int_Y2           8  9522   1.23 1.96   0.00    0.79  0.00   0.00  16.00 16.00
## intt_Y2          9  9519   0.00 1.96  -1.02   -0.42  0.63  -1.70  15.03 16.73
## age_Y3          10  8825 154.93 7.77 155.00  154.83 10.38 137.00 175.00 38.00
## int_Y3          11  8821   1.44 2.15   1.00    0.97  1.48   0.00  15.00 15.00
## intt_Y3         12  8819   0.00 2.15  -0.67   -0.44  1.18  -1.82  13.69 15.52
##               skew kurtosis   se
## age_Baseline  0.07    -1.26 0.07
## int_Baseline  2.52     8.16 0.02
## intt_Baseline 2.51     8.15 0.02
## age_Y1        0.07    -1.18 0.08
## int_Y1        2.42     7.28 0.02
## intt_Y1       2.42     7.26 0.02
## age_Y2        0.11    -0.93 0.08
## int_Y2        2.38     7.12 0.02
## intt_Y2       2.36     7.07 0.02
## age_Y3        0.09    -1.02 0.08
## int_Y3        2.14     5.47 0.02
## intt_Y3       2.12     5.38 0.02

library(ggplot2)

## 
## Attaching package: 'ggplot2'

## The following objects are masked from 'package:psych':
## 
##     %+%, alpha

# Create four-panel histogram
library(ggplot2)

# Combine all int variables into a single column
all_int <- c(data_frame$int_Baseline, data_frame$int_Y1, data_frame$int_Y2, data_frame$int_Y3)

# Create a data frame with the combined int values
combined_data <- data.frame(int = all_int, Timepoint = rep(c("Baseline", "Y1", "Y2", "Y3"), each = nrow(data_frame)))

# Create the combined histogram with APA-style formatting
ggplot(combined_data, aes(x = int)) +
  geom_histogram(binwidth = 1, fill = "#0072B2", color = "#0072B2", alpha = 0.7) +
  labs(title = "Histogram Internalizing Depression Symptoms Across Study Timepoints", x = "int", y = "Frequency") +
  facet_wrap(~ Timepoint, scales = "free_x", nrow = 2) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        panel.border = element_rect(color = "black", fill = NA),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        strip.text = element_text(size = 12),
        plot.title = element_text(size = 14, hjust = 0.5),
        strip.background = element_rect(fill = "#E5E5E5"),
        legend.position = "none")

## Warning: Removed 2972 rows containing non-finite values (`stat_bin()`).

################################################################################
# install.packages("corrplot")
library(corrplot)

## corrplot 0.92 loaded

library(dplyr)
library(ggplot2)
library(reshape2)  

## 
## Attaching package: 'reshape2'

## The following objects are masked from 'package:data.table':
## 
##     dcast, melt

## The following object is masked from 'package:tidyr':
## 
##     smiths

# Select the int variables
int_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3")

# Subset the data for the selected int variables
int_data <- data_frame %>%
  select(all_of(int_variables))

# Compute the correlation matrix
cor_matrix <- cor(int_data, use = "complete.obs")
cor_matrix

##              int_Baseline    int_Y1    int_Y2    int_Y3
## int_Baseline    1.0000000 0.6275352 0.5472477 0.4613667
## int_Y1          0.6275352 1.0000000 0.6263788 0.5508441
## int_Y2          0.5472477 0.6263788 1.0000000 0.6314528
## int_Y3          0.4613667 0.5508441 0.6314528 1.0000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 4) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

################################################################################

# Convert to long to examine trajectories
library(tidyr)

# Subset 
long_data <- data_frame[, c("IID", "int_Baseline", "int_Y1", "int_Y2", "int_Y3")]

library(reshape2)

# Convert wide data to long format using melt()
long_data <- melt(data_frame, id.vars = "IID", measure.vars = c("int_Baseline", "int_Y1", "int_Y2", "int_Y3"),
                  variable.name = "Timepoint", value.name = "int")

# Sort the long-format data by IID
sorted_long_data <- long_data %>%
  arrange(IID)

# Print the long-format data
# print(long_data)

library(dplyr)
library(ggplot2)

# Randomly select 1000 unique IIDs
unique_iids <- sorted_long_data %>%
  distinct(IID) %>%
  sample_n(200)  # Select 1000 random IIDs

# Subset the data based on the selected IIDs
subset_data <- sorted_long_data %>%
  filter(IID %in% unique_iids$IID)

# Create a longitudinal plot of int across timepoints
ggplot(subset_data, aes(x = Timepoint, y = int, group = IID, color = IID)) +
  geom_line(size = 1) +
  labs(title = "Longitudinal Plot of Internalizing Depression Symptoms Across Timepoints", x = "Timepoint", y = "int") +
  theme_minimal() +
  theme(legend.position = "none",
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_rect(color = "black", fill = NA),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        plot.title = element_text(size = 14, hjust = 0.5))

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Warning: Removed 43 rows containing missing values (`geom_line()`).

Waist Circumference to Height Ratio (wchr)

#Load anthropometric data
anth <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/physical-health/ph_y_anthro.csv", header = TRUE, sep = ",", dec = ".")
#View(anth)
library(psych)
#describe(anth$anthro_waist_cm) #Waist Circumference (inches)
#describe(anth$anthroheightcalc) #Standing Height Average (inches)

#Create key for Identifiers:
anth.varlabels <- anth[1,]

#Remove first row of Identifiers so we are left with only the data:
anth.data <- anth[-1,]

#Rename subject ID
anth.data$IID  <- anth.data[,"src_subject_id"]

#Create 0, 1, 2, 3 assessment data sets
Baseline.anth<-anth.data[anth.data$eventname=="baseline_year_1_arm_1",]
Y1.anth<-anth.data[anth.data$eventname=="1_year_follow_up_y_arm_1",]
Y2.anth<-anth.data[anth.data$eventname=="2_year_follow_up_y_arm_1",]
Y3.anth<-anth.data[anth.data$eventname=="3_year_follow_up_y_arm_1",]

###############################################################################
################################ Baseline (10.5)###############################
###############################################################################

# First, merge Baseline.anth with Baseline.Identifiers based on IID
Merged.Baseline_anth_identifiers <- merge(Baseline.anth, Baseline.Identifiers, by = "IID")

# Then, merge Merged.Baseline_anth_identifiers with baseline.demo based on IID to get sex variable
Merged.Baseline_ID_anth <- merge(Merged.Baseline_anth_identifiers, Baseline.demo, by = "IID")

#Create Waist Circumference to Height Ratio Variable
Merged.Baseline_ID_anth$wchr <- Merged.Baseline_ID_anth$anthro_waist_cm/Merged.Baseline_ID_anth$anthroheightcalc

# Examine extreme scores
library(ggplot2)
summary(Merged.Baseline_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.2400  0.4314  0.4655  0.4811  0.5157  5.7500      14

Merged.Baseline_ID_anth <- Merged.Baseline_ID_anth[Merged.Baseline_ID_anth$wchr >= .20 & Merged.Baseline_ID_anth$wchr <= 1.5, ]
summary(Merged.Baseline_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.2400  0.4314  0.4655  0.4801  0.5156  1.3722      14

histogram_plot <- ggplot(Merged.Baseline_ID_anth, aes(x = wchr)) +
  geom_histogram(binwidth = .05, fill = "blue", color = "black") +
  labs(title = "Histogram of wchr", x = "wchr", y = "Frequency") +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 14),
    axis.title = element_text(size = 12),
    axis.text = element_text(size = 10)
  )
print(histogram_plot)

## Warning: Removed 14 rows containing non-finite values (`stat_bin()`).

# Regress age out of wchr score by sex separately
library(modelr)
library(tidyr)
library(dplyr)

Merged.Baseline_ID_anth$age <- Merged.Baseline_ID_anth$interview_age

# Subset the data
subset_data <- Merged.Baseline_ID_anth[, c("IID", "age", "sex", "wchr")]
# Make data set for boys and girls
boys_data <- subset_data[subset_data$sex == 1, ]
girls_data <- subset_data[subset_data$sex == 2, ]

######################## Regress wchr scores for boys ###########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on wchr and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
boys_data$wchrt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress wchr scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on wchr and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
girls_data$wchrt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine wchrt variables and create a new combined wchrt column
merged_data <- merged_data %>%
  mutate(wchrt = coalesce(wchrt.boys, wchrt.girls))

# Display the merged data with combined wchrt variable
# print(merged_data)

# Subset to keep only IDD and wchrt score
merged_data <- merged_data[, c("IID", "wchrt")]

# Merge with raw data
merged_wchr <- merge(merged_data, Merged.Baseline_ID_anth, by = "IID", all = TRUE)
# print(merged_wchr)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Baseline <- c("IID","wchr","wchrt","age", "anthro_waist_cm", "anthroheightcalc")

 # Convert the data frame to a data.table
setDT(merged_wchr)

# Subset the data table and create a new data table
subset_data <- merged_wchr[, ..variables_to_keep_Baseline]

# Rename the columns by appending "_Baseline"
colnames(subset_data) <- paste0(colnames(subset_data), "_Baseline")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Baseline"] <- "IID"

# rename data set for merge
wchr_Baseline <- subset_data

###############################################################################
################################ Year 1 (11.5) ################################
###############################################################################

# First, merge Y1.anth with Y1.Identifiers based on IID
Merged.Y1_anth_identifiers <- merge(Y1.anth, Y1.Identifiers, by = "IID")

# Then, merge Merged.Y1_anth_identifiers with Y1.demo based on IID to get sex variable
Merged.Y1_ID_anth <- merge(Merged.Y1_anth_identifiers, Baseline.demo, by = "IID")

#Create Waist Circumference to Height Ratio Variable
Merged.Y1_ID_anth$wchr <- Merged.Y1_ID_anth$anthro_waist_cm/Merged.Y1_ID_anth$anthroheightcalc

# Examine extreme scores
library(ggplot2)
summary(Merged.Y1_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.0000  0.4304  0.4651  0.4821  0.5176  5.3333      42

Merged.Y1_ID_anth <- Merged.Y1_ID_anth[Merged.Y1_ID_anth$wchr >= .20 & Merged.Y1_ID_anth$wchr <= 1.5, ]
summary(Merged.Y1_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.2656  0.4304  0.4652  0.4816  0.5175  1.4746      42

histogram_plot <- ggplot(Merged.Y1_ID_anth, aes(x = wchr)) +
  geom_histogram(binwidth = .05, fill = "blue", color = "black") +
  labs(title = "Histogram of wchr", x = "wchr", y = "Frequency") +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 14),
    axis.title = element_text(size = 12),
    axis.text = element_text(size = 10)
  )
print(histogram_plot)

## Warning: Removed 42 rows containing non-finite values (`stat_bin()`).

# Regress age out of wchr score by sex separately
library(modelr)
library(tidyr)
library(dplyr)

Merged.Y1_ID_anth$age <- Merged.Y1_ID_anth$interview_age

# Subset the data
subset_data <- Merged.Y1_ID_anth[, c("IID", "age", "sex", "wchr")]
# Make data set for boys and girls
boys_data <- subset_data[subset_data$sex == 1, ]
girls_data <- subset_data[subset_data$sex == 2, ]

######################## Regress wchr scores for boys ###########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on wchr and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
boys_data$wchrt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress wchr scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on wchr and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
girls_data$wchrt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine wchrt variables and create a new combined wchrt column
merged_data <- merged_data %>%
  mutate(wchrt = coalesce(wchrt.boys, wchrt.girls))

# Display the merged data with combined wchrt variable
# print(merged_data)

# Subset to keep only IDD and wchrt score
merged_data <- merged_data[, c("IID", "wchrt")]

# Merge with raw data
merged_wchr <- merge(merged_data, Merged.Y1_ID_anth , by = "IID", all = TRUE)
# print(merged_wchr)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y1 <- c("IID","wchr","wchrt","age","anthro_waist_cm", "anthroheightcalc")

# Convert the data frame to a data.table
setDT(merged_wchr)

# Subset the data table and create a new data table
subset_data <- merged_wchr[, ..variables_to_keep_Y1]

# Rename the columns by appending "_Y1"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y1")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y1"] <- "IID"

# rename data set for merge
wchr_Y1 <- subset_data

###############################################################################
################################ Year 2 (12.5) ################################
###############################################################################

# First, merge Y2.anth with Y2.Identifiers based on IID
Merged.Y2_anth_identifiers <- merge(Y2.anth, Y2.Identifiers, by = "IID")

# Then, merge Merged.Y2_anth_identifiers with Y2.demo based on IID to get sex variable
Merged.Y2_ID_anth <- merge(Merged.Y2_anth_identifiers, Baseline.demo, by = "IID")

#Create Waist Circumference to Height Ratio Variable
Merged.Y2_ID_anth$wchr <- Merged.Y2_ID_anth$anthro_waist_cm/Merged.Y2_ID_anth$anthroheightcalc

# Examine extreme scores
library(ggplot2)
summary(Merged.Y2_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.0000  0.4272  0.4643  0.4820  0.5226  4.6154     161

Merged.Y2_ID_anth <- Merged.Y2_ID_anth %>% filter(wchr >= 0.2)
Merged.Y2_ID_anth <- Merged.Y2_ID_anth %>% filter(wchr <= 1.5)
summary(Merged.Y2_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2594  0.4273  0.4643  0.4816  0.5226  1.4062

histogram_plot <- ggplot(Merged.Y2_ID_anth, aes(x = wchr)) +
  geom_histogram(binwidth = .05, fill = "blue", color = "black") +
  labs(title = "Histogram of wchr", x = "wchr", y = "Frequency") +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 14),
    axis.title = element_text(size = 12),
    axis.text = element_text(size = 10)
  )
print(histogram_plot)

# Regress age out of wchr score by sex separately
library(modelr)
library(tidyr)
library(dplyr)

Merged.Y2_ID_anth$age <- Merged.Y2_ID_anth$interview_age

# Subset the data
subset_data <- Merged.Y2_ID_anth[, c("IID", "age", "sex", "wchr")]
# Make data set for boys and girls
boys_data <- subset_data[subset_data$sex == 1, ]
girls_data <- subset_data[subset_data$sex == 2, ]

######################## Regress wchr scores for boys ###########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on wchr and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
boys_data$wchrt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress wchr scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on wchr and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
girls_data$wchrt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine wchrt variables and create a new combined wchrt column
merged_data <- merged_data %>%
  mutate(wchrt = coalesce(wchrt.boys, wchrt.girls))

# Display the merged data with combined wchrt variable
# print(merged_data)

# Subset to keep only IDD and wchrt score
merged_data <- merged_data[, c("IID","wchrt")]

# Merge with CDC calculated data set
merged_wchr <- merge(merged_data, Merged.Y2_ID_anth , by = "IID", all = TRUE)
# print(merged_wchr)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y2 <- c("IID","wchr","wchrt","age","anthro_waist_cm", "anthroheightcalc")

# Convert the data frame to a data.table
setDT(merged_wchr)

# Subset the data table and create a new data table
subset_data <- merged_wchr[, ..variables_to_keep_Y2]

# Rename the columns by appending "_Y2"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y2")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y2"] <- "IID"

# rename data set for merge
wchr_Y2 <- subset_data

###############################################################################
################################ Year 3 (13.5) ################################
###############################################################################


# First, merge Y3.anth with Y3.Identifiers based on IID
Merged.Y3_anth_identifiers <- merge(Y3.anth, Y3.Identifiers, by = "IID")

# Then, merge Merged.Y3_anth_identifiers with Y3.demo based on IID to get sex variable
Merged.Y3_ID_anth <- merge(Merged.Y3_anth_identifiers, Baseline.demo, by = "IID")

#Create Waist Circumference to Height Ratio Variable
Merged.Y3_ID_anth$wchr <- Merged.Y3_ID_anth$anthro_waist_cm/Merged.Y3_ID_anth$anthroheightcalc

# Examine extreme scores
library(ggplot2)
summary(Merged.Y3_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.0000  0.4291  0.4685  0.4925  0.5342  5.5000    1795

Merged.Y3_ID_anth <- Merged.Y3_ID_anth %>% filter(wchr >= 0.2)
Merged.Y3_ID_anth <- Merged.Y3_ID_anth %>% filter(wchr <= 1.5)
summary(Merged.Y3_ID_anth$wchr)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3437  0.4295  0.4686  0.4904  0.5341  1.2629

histogram_plot <- ggplot(Merged.Y3_ID_anth, aes(x = wchr)) +
  geom_histogram(binwidth = .05, fill = "blue", color = "black") +
  labs(title = "Histogram of wchr", x = "wchr", y = "Frequency") +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 14),
    axis.title = element_text(size = 12),
    axis.text = element_text(size = 10)
  )
print(histogram_plot)

# Regress age out of wchr score by sex separately
library(modelr)
library(tidyr)
library(dplyr)

Merged.Y3_ID_anth$age <- Merged.Y3_ID_anth$interview_age

# Subset the data
subset_data <- Merged.Y3_ID_anth[, c("IID", "age", "sex", "wchr")]
# Make data set for boys and girls
boys_data <- subset_data[subset_data$sex == 1, ]
girls_data <- subset_data[subset_data$sex == 2, ]

######################## Regress wchr scores for boys ###########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on wchr and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
boys_data$wchrt <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress wchr scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on wchr and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$wchr), ]

# Fit the linear regression model
model <- lm(wchr ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals into wchrt var
girls_data$wchrt <- residuals

# Display the modified data table with residuals
# print(girls_data)

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine wchrt variables and create a new combined wchrt column
merged_data <- merged_data %>%
  mutate(wchrt = coalesce(wchrt.boys, wchrt.girls))

# Display the merged data with combined wchrt variable
# print(merged_data)

# Subset to keep only IDD and wchrt score
merged_data <- merged_data[, c("IID", "wchrt")]

# Merge with raw data
merged_wchr <- merge(merged_data, Merged.Y3_ID_anth , by = "IID", all = TRUE)
# print(merged_wchr)

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y3 <- c("IID","wchr","wchrt","age","anthro_waist_cm", "anthroheightcalc")

# Convert the data frame to a data.table
setDT(merged_wchr)

# Subset the data table and create a new data table
subset_data <- merged_wchr[, ..variables_to_keep_Y3]

# Rename the columns by appending "_Y3"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y3")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y3"] <- "IID"

# rename data set for merge
wchr_Y3 <- subset_data

##### Merge all Waist Height to Weight Ratio Together data sets together  ######

# Merge all wchr data sets together
library(data.table)

# List of datasets to merge
wchr_datasets <- list(wchr_Baseline, wchr_Y1, wchr_Y2, wchr_Y3)

# Merge all data.tables using full outer join based on IID
wchr_merged_data <- Reduce(function(x, y) merge(x, y, by = "IID", all = TRUE), wchr_datasets)

Descriptives (wchr)

# wchr Descriptive Statistics
library(psych)

# Select the variables you want to describe
variables_to_describe <- c("age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3")

# Convert data.table to data frame
data_frame <- as.data.frame(wchr_merged_data)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars     n   mean   sd median trimmed   mad    min    max range
## age_Baseline      1 10345 118.98 7.49 119.00  118.87 10.38 107.00 133.00 26.00
## wchr_Baseline     2 10345   0.48 0.07   0.47    0.47  0.06   0.24   1.37  1.13
## wchrt_Baseline    3 10342   0.00 0.07  -0.01   -0.01  0.06  -0.24   0.89  1.13
## age_Y1            4  9714 131.07 7.72 131.00  130.99 10.38 117.00 149.00 32.00
## wchr_Y1           5  9714   0.48 0.08   0.47    0.47  0.06   0.27   1.47  1.21
## wchrt_Y1          6  9711   0.00 0.08  -0.02   -0.01  0.06  -0.21   1.00  1.21
## age_Y2            7  7919 143.77 7.85 144.00  143.70 10.38 127.00 166.00 39.00
## wchr_Y2           8  7919   0.48 0.08   0.46    0.47  0.07   0.26   1.41  1.15
## wchrt_Y2          9  7917   0.00 0.08  -0.02   -0.01  0.07  -0.22   0.92  1.14
## age_Y3           10  1755 155.33 7.45 155.00  155.34  8.90 139.00 174.00 35.00
## wchr_Y3          11  1755   0.49 0.09   0.47    0.48  0.07   0.34   1.26  0.92
## wchrt_Y3         12  1754   0.00 0.08  -0.02   -0.01  0.07  -0.15   0.77  0.92
##                skew kurtosis   se
## age_Baseline   0.07    -1.26 0.07
## wchr_Baseline  1.31     4.92 0.00
## wchrt_Baseline 1.31     4.92 0.00
## age_Y1         0.07    -1.19 0.08
## wchr_Y1        2.05    13.96 0.00
## wchrt_Y1       2.05    13.98 0.00
## age_Y2         0.08    -1.01 0.09
## wchr_Y2        1.52     6.84 0.00
## wchrt_Y2       1.52     6.77 0.00
## age_Y3         0.01    -1.08 0.18
## wchr_Y3        1.72     7.24 0.00
## wchrt_Y3       1.72     7.30 0.00

# Create four-panel histogram
library(ggplot2)

# Combine all wchr variables into a single column
all_wchr <- c(data_frame$wchr_Baseline, data_frame$wchr_Y1, data_frame$wchr_Y2, data_frame$wchr_Y3)

# Create a data frame with the combined wchr values
combined_data <- data.frame(wchr = all_wchr, Timepoint = rep(c("Baseline", "Y1", "Y2", "Y3"), each = nrow(data_frame)))

# Create the combined histogram with APA-style formatting
ggplot(combined_data, aes(x = wchr)) +
  geom_histogram(binwidth = .5, fill = "#0072B2", color = "#0072B2", alpha = 0.7) +
  labs(title = "Histogram of Combined wchr", x = "wchr", y = "Frequency") +
  facet_wrap(~ Timepoint, scales = "free_x", nrow = 2) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        panel.border = element_rect(color = "black", fill = NA),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        strip.text = element_text(size = 12),
        plot.title = element_text(size = 14, hjust = 0.5),
        strip.background = element_rect(fill = "#E5E5E5"),
        legend.position = "none")

## Warning: Removed 14075 rows containing non-finite values (`stat_bin()`).

################################################################################
# install.packages("corrplot")
library(corrplot)
library(dplyr)
library(ggplot2)
library(reshape2)  

# Select the wchr variables
wchr_variables <- c("wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3")

# Subset the data for the selected wchr variables
wchr_data <- data_frame %>%
  select(all_of(wchr_variables))

# Compute the correlation matrix
cor_matrix <- cor(wchr_data, use = "complete.obs")
cor_matrix

##               wchr_Baseline   wchr_Y1   wchr_Y2   wchr_Y3
## wchr_Baseline     1.0000000 0.7383546 0.7041304 0.6793967
## wchr_Y1           0.7383546 1.0000000 0.7886294 0.7572817
## wchr_Y2           0.7041304 0.7886294 1.0000000 0.7901607
## wchr_Y3           0.6793967 0.7572817 0.7901607 1.0000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 4) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

################################################################################

# Convert to long to examine trajectories
library(tidyr)

# Subset 
long_data <- data_frame[, c("IID", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3")]

library(reshape2)

# Convert wide data to long format using melt()
long_data <- melt(data_frame, id.vars = "IID", measure.vars = c("wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3"),
                  variable.name = "Timepoint", value.name = "wchr")

# Sort the long-format data by IID
sorted_long_data <- long_data %>%
  arrange(IID)

# Print the long-format data
# print(long_data)

library(dplyr)
library(ggplot2)

# Randomly select 1000 unique IIDs
unique_iids <- sorted_long_data %>%
  distinct(IID) %>%
  sample_n(200)  # Select 1000 random IIDs

# Subset the data based on the selected IIDs
subset_data <- sorted_long_data %>%
  filter(IID %in% unique_iids$IID)

# Create a longitudinal plot of wchr across timepoints
ggplot(subset_data, aes(x = Timepoint, y = wchr, group = IID, color = IID)) +
  geom_line(size = 1) +
  labs(title = "Longitudinal Plot of wchr Across Timepoint (Subset)", x = "Timepoint", y = "wchr") +
  theme_minimal() +
  theme(legend.position = "none",
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_rect(color = "black", fill = NA),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        plot.title = element_text(size = 14, hjust = 0.5))

## Warning: Removed 202 rows containing missing values (`geom_line()`).

Puberty - Pubertal Development Scale (pub)

#Load PDS data
pub <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/physical-health/ph_y_pds.csv", header = TRUE, sep = ",", dec = ".")
#View(pds)

describe(pub$pds_y_ss_female_category) 

##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 6445 2.41 0.91      3    2.41 1.48   1   5     4 -0.22    -0.79 0.01

describe(pub$pds_y_ss_male_category) 

##    vars    n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 8242 1.95 0.77      2    1.92 1.48   1   5     4  0.4    -0.29 0.01

describe(pub$pds_y_ss_female_category_2) 

##    vars     n mean sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 20170 3.09  1      3    3.19 1.48   1   5     4 -0.56    -0.25 0.01

describe(pub$pds_y_ss_male_cat_2) 

##    vars     n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 24190  2.3 0.89      2    2.27 1.48   1   5     4 0.15    -0.68 0.01

#Create key for Identifiers:
pub.varlabels <- pub[1,]

#Remove first row of Identifiers so we are left with only the data:
pub.data <- pub[-1,]

#Rename subject ID
pub.data$IID  <- pub.data[,"src_subject_id"]

#Create 0, 1, 2,3 assessment data sets
Baseline.pub<-pub.data[pub.data$eventname=="baseline_year_1_arm_1",]
Y1.pub<-pub.data[pub.data$eventname=="1_year_follow_up_y_arm_1",]
Y2.pub<-pub.data[pub.data$eventname=="2_year_follow_up_y_arm_1",]
Y3.pub<-pub.data[pub.data$eventname=="3_year_follow_up_y_arm_1",]

###############################################################################
################################ Baseline (10.5)###############################
###############################################################################

# Merge Baseline.pub with Baseline.Identifiers based on IID to get age
Merged.Baseline_pub_identifiers <- merge(Baseline.pub, Baseline.Identifiers, by = "IID")

# Then, merge Merged.Baseline_pub_identifiers with baseline.demo based on IID to get sex variable
Merged.Baseline_ID_pub <- merge(Merged.Baseline_pub_identifiers, Baseline.demo, by = "IID")

############### Regress age out of BMI score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

# Rename variables for code below
colnames(Merged.Baseline_ID_pub)[colnames(Merged.Baseline_ID_pub) == "interview_age"] <- "age"
colnames(Merged.Baseline_ID_pub)[colnames(Merged.Baseline_ID_pub) == "pds_y_ss_female_category"] <- "pub_girls"
colnames(Merged.Baseline_ID_pub)[colnames(Merged.Baseline_ID_pub) == "pds_y_ss_male_category"] <- "pub_boys"

# Subset the data
pub_subset <- Merged.Baseline_ID_pub[, c("IID", "age", "sex", "pub_girls", "pub_boys" )]

# Make data set for boys and girls
boys_data <- pub_subset[pub_subset$sex == 1, ]
girls_data <- pub_subset[pub_subset$sex == 2, ]

#################### Regress PDS scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on pub and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$pub_boys), ]

# Fit the linear regression model
model <- lm(pub_boys ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
boys_data$pubt_boys <- residuals

# Display the modified data table with residuals
#print(boys_data)

######################## Regress pub scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on pub and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$pub_girls), ]

# Fit the linear regression model
model <- lm(pub_girls ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
girls_data$pubt_girls <- residuals

# Display the modified data table with residuals
# print(girls_data)

################################################################################

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine pubt variables and create a new combined pubt column
merged_data <- merged_data %>%
  mutate(pubt = coalesce(pubt_boys, pubt_girls))

# Display the merged data with combined pubt variable
# print(merged_data)

# Subset to only IDD and pubt score
merged_data <- merged_data[, c("IID", "pubt")]

# Merge with raw pub data
merged_pub <- merge(pub_subset, merged_data, by = "IID", all = TRUE)
# print(merged_pub)

# Combine pub boys and girls variables and create a new combined pub column
merged_pub <- merged_pub %>%
  mutate(pub = coalesce(pub_boys, pub_girls))

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Baseline <- c("IID","pub", "pubt", "age")

# Convert the data frame to a data.table
setDT(merged_pub)

# Subset the data table and create a new data table
subset_data <- merged_pub[, ..variables_to_keep_Baseline]

# Rename the columns by appending "_Baseline"
colnames(subset_data) <- paste0(colnames(subset_data), "_Baseline")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Baseline"] <- "IID"

# rename data set for merge
pub_Baseline <- subset_data

###############################################################################
################################ Year 1 (11.5) ################################
###############################################################################

# Merge Y1.pub with Baseline.Identifiers based on IID to get age
Merged.Y1_pub_identifiers <- merge(Y1.pub, Baseline.Identifiers, by = "IID")

# Then, merge Merged.Baseline_pub_identifiers with baseline.demo based on IID to get sex variable
Merged.Y1_ID_pub <- merge(Merged.Y1_pub_identifiers, Baseline.demo, by = "IID")

############### Regress age out of PDS score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

# Rename variables for code below
colnames(Merged.Y1_ID_pub)[colnames(Merged.Y1_ID_pub) == "interview_age"] <- "age"
colnames(Merged.Y1_ID_pub)[colnames(Merged.Y1_ID_pub) == "pds_y_ss_female_category"] <- "pub_girls"
colnames(Merged.Y1_ID_pub)[colnames(Merged.Y1_ID_pub) == "pds_y_ss_male_category"] <- "pub_boys"

# Subset the data
pub_subset <- Merged.Y1_ID_pub[, c("IID", "age", "sex", "pub_girls", "pub_boys" )]

# Make data set for boys and girls
boys_data <- pub_subset[pub_subset$sex == 1, ]
girls_data <- pub_subset[pub_subset$sex == 2, ]

#################### Regress PDS scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on pub and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$pub_boys), ]

# Fit the linear regression model
model <- lm(pub_boys ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
boys_data$pubt_boys <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress pub scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on pub and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$pub_girls), ]

# Fit the linear regression model
model <- lm(pub_girls ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
girls_data$pubt_girls <- residuals

# Display the modified data table with residuals
# print(girls_data)

################################################################################

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine pubt variables and create a new combined pubt column
merged_data <- merged_data %>%
  mutate(pubt = coalesce(pubt_boys, pubt_girls))

# Display the merged data with combined pubt variable
# print(merged_data)

# Subset to only IDD and pubt score
merged_data <- merged_data[, c("IID", "pubt")]

# Merge with raw pub data
merged_pub <- merge(pub_subset, merged_data, by = "IID", all = TRUE)
# print(merged_pub)

# Combine pub boys and girls variables and create a new combined pub column
merged_pub <- merged_pub %>%
  mutate(pub = coalesce(pub_boys, pub_girls))

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y1 <- c("IID","pub", "pubt", "age")

# Convert the data frame to a data.table
setDT(merged_pub)

# Subset the data table and create a new data table
subset_data <- merged_pub[, ..variables_to_keep_Y1]

# Rename the columns by appending "_Y1"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y1")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y1"] <- "IID"

# rename data set for merge
pub_Y1 <- subset_data

###############################################################################
################################ Year 2 (12.5) ################################
###############################################################################

# Merge Y2.pub with Baseline.Identifiers based on IID to get age
Merged.Y2_pub_identifiers <- merge(Y2.pub, Y2.Identifiers, by = "IID")

# Then, merge Merged.Baseline_pub_identifiers with baseline.demo based on IID to get sex variable
Merged.Y2_ID_pub <- merge(Merged.Y2_pub_identifiers, Baseline.demo, by = "IID")

############### Regress age out of PDS score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

#NOTE USING _2 PDS score since massive missing on one without _2 NEED TO KNOW DIFFERENCES

# Rename variables for code below
colnames(Merged.Y2_ID_pub)[colnames(Merged.Y2_ID_pub) == "interview_age"] <- "age"
colnames(Merged.Y2_ID_pub)[colnames(Merged.Y2_ID_pub) == "pds_y_ss_female_category_2"] <- "pub_girls"
colnames(Merged.Y2_ID_pub)[colnames(Merged.Y2_ID_pub) == "pds_y_ss_male_cat_2"] <- "pub_boys"

#summary(Merged.Y2_ID_pub$pub_boys)

# Subset the data
pub_subset <- Merged.Y2_ID_pub[, c("IID", "age", "sex", "pub_girls", "pub_boys")]

# Make data set for boys and girls
boys_data <- pub_subset[pub_subset$sex == 1, ]
girls_data <- pub_subset[pub_subset$sex == 2, ]

#################### Regress PDS scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on pub and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$pub_boys), ]

# Fit the linear regression model
model <- lm(pub_boys ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
boys_data$pubt_boys <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress pub scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on pub and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$pub_girls), ]

# Fit the linear regression model
model <- lm(pub_girls ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
girls_data$pubt_girls <- residuals

# Display the modified data table with residuals
# print(girls_data)

################################################################################

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine pubt variables and create a new combined pubt column
merged_data <- merged_data %>%
  mutate(pubt = coalesce(pubt_boys, pubt_girls))

# Display the merged data with combined pubt variable
# print(merged_data)

# Subset to only IDD and pubt score
merged_data <- merged_data[, c("IID", "pubt")]

# Merge with raw pub data
merged_pub <- merge(pub_subset, merged_data, by = "IID", all = TRUE)
# print(merged_pub)

# Combine pub boys and girls variables and create a new combined pub column
merged_pub <- merged_pub %>%
  mutate(pub = coalesce(pub_boys, pub_girls))

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y2 <- c("IID","pub", "pubt", "age")

# Convert the data frame to a data.table
setDT(merged_pub)

# Subset the data table and create a new data table
subset_data <- merged_pub[, ..variables_to_keep_Y2]

# Rename the columns by appending "_Y2"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y2")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y2"] <- "IID"

# rename data set for merge
pub_Y2 <- subset_data

###############################################################################
################################ Year 3 (13.5) ################################
###############################################################################

# Merge Y3.pub with Baseline.Identifiers based on IID to get age
Merged.Y3_pub_identifiers <- merge(Y3.pub, Baseline.Identifiers, by = "IID")

# Then, merge Merged.Baseline_pub_identifiers with baseline.demo based on IID to get sex variable
Merged.Y3_ID_pub <- merge(Merged.Y3_pub_identifiers, Baseline.demo, by = "IID")

############### Regress age out of BMI score by sex separately #################
library(modelr)
library(tidyr)
library(dplyr)

# summary(Merged.Y3_ID_pub$pds_y_ss_female_category)
# summary(Merged.Y3_ID_pub$pds_y_ss_female_category_2) #Use this one

# summary(Merged.Y3_ID_pub$pds_y_ss_male_category)
# summary(Merged.Y3_ID_pub$pds_y_ss_male_cat_2) #Use this one

# Rename variables for code below
colnames(Merged.Y3_ID_pub)[colnames(Merged.Y3_ID_pub) == "interview_age"] <- "age"
colnames(Merged.Y3_ID_pub)[colnames(Merged.Y3_ID_pub) == "pds_y_ss_female_category_2"] <- "pub_girls"
colnames(Merged.Y3_ID_pub)[colnames(Merged.Y3_ID_pub) == "pds_y_ss_male_cat_2"] <- "pub_boys"

# Subset the data
pub_subset <- Merged.Y3_ID_pub[, c("IID", "age", "sex", "pub_girls", "pub_boys" )]

# Make data set for boys and girls
boys_data <- pub_subset[pub_subset$sex == 1, ]
girls_data <- pub_subset[pub_subset$sex == 2, ]

#################### Regress PDS scores for boys #####################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(boys_data)

# Drop cases missing on pub and age
boys_data <- boys_data[!is.na(boys_data$age) & !is.na(boys_data$pub_boys), ]

# Fit the linear regression model
model <- lm(pub_boys ~ age, data = boys_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
boys_data$pubt_boys <- residuals

# Display the modified data table with residuals
# print(boys_data)

######################## Regress pub scores for girls ##########################

# Convert data.table to data.frame for linear regression
data_frame <- as.data.frame(girls_data)

# Drop cases missing on pub and age
girls_data <- girls_data[!is.na(girls_data$age) & !is.na(girls_data$pub_girls), ]

# Fit the linear regression model
model <- lm(pub_girls ~ age, data = girls_data)

# Calculate residuals
residuals <- residuals(model)

# Save residuals pubo pubt var
girls_data$pubt_girls <- residuals

# Display the modified data table with residuals
# print(girls_data)

################################################################################

# Merge Data
merged_data <- merge(boys_data, girls_data, by = "IID", all = TRUE, suffixes = c(".boys", ".girls"))

# Combine pubt variables and create a new combined pubt column
merged_data <- merged_data %>%
  mutate(pubt = coalesce(pubt_boys, pubt_girls))

# Display the merged data with combined pubt variable
# print(merged_data)

# Subset to only IDD and pubt score
merged_data <- merged_data[, c("IID", "pubt")]

# Merge with raw pub data
merged_pub <- merge(pub_subset, merged_data, by = "IID", all = TRUE)
# print(merged_pub)

# Combine pub boys and girls variables and create a new combined pub column
merged_pub <- merged_pub %>%
  mutate(pub = coalesce(pub_boys, pub_girls))

# Rename variables to keep in each assessment data set
library(data.table)
variables_to_keep_Y3 <- c("IID","pub", "pubt", "age")

# Convert the data frame to a data.table
setDT(merged_pub)

# Subset the data table and create a new data table
subset_data <- merged_pub[, ..variables_to_keep_Y3]

# Rename the columns by appending "_Y3"
colnames(subset_data) <- paste0(colnames(subset_data), "_Y3")

# Rename IID for merge
colnames(subset_data)[colnames(subset_data) == "IID_Y3"] <- "IID"

# rename data set for merge
pub_Y3 <- subset_data

############### Merge all PDS data sets together  ####################

# Merge all pub data sets together
library(data.table)

# List of datasets to merge
pub_datasets <- list(pub_Baseline, pub_Y1, pub_Y2, pub_Y3)

# Merge all data.tables using full outer join based on IID
pub_merged_data <- Reduce(function(x, y) merge(x, y, by = "IID", all = TRUE), pub_datasets)

Descriptives

# Puberty Descriptive Statistics
library(psych)

# Select the variables you want to describe
variables_to_describe <- c("age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3")

# Convert data.table to data frame
data_frame <- as.data.frame(pub_merged_data)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##               vars     n   mean   sd median trimmed   mad    min    max range
## age_Baseline     1 10366 118.97 7.49 119.00  118.87 10.38 107.00 133.00 26.00
## pub_Baseline     2  8397   2.08 0.83   2.00    2.06  1.48   1.00   5.00  4.00
## pubt_Baseline    3  8363   0.00 0.81   0.05   -0.01  1.05  -1.61   3.08  4.69
## age_Y1           4  9802 118.97 7.51 119.00  118.87 10.38 107.00 133.00 26.00
## pub_Y1           5  4247   2.27 0.90   2.00    2.25  1.48   1.00   5.00  4.00
## pubt_Y1          6  4224   0.00 0.80   0.04    0.00  0.95  -2.12   3.08  5.21
## age_Y2           7  9585 144.30 8.02 144.00  144.20 10.38 127.00 168.00 41.00
## pub_Y2           8  9067   2.69 0.97   3.00    2.73  1.48   1.00   5.00  4.00
## pubt_Y2          9  9064   0.00 0.77   0.04    0.02  0.75  -2.84   3.02  5.86
## age_Y3          10  9027 118.97 7.50 119.00  118.87 10.38 107.00 133.00 26.00
## pub_Y3          11  8595   3.12 0.93   3.00    3.20  1.48   1.00   5.00  4.00
## pubt_Y3         12  8592   0.00 0.74   0.11    0.03  0.69  -2.94   2.53  5.47
##                skew kurtosis   se
## age_Baseline   0.07    -1.26 0.07
## pub_Baseline   0.19    -0.75 0.01
## pubt_Baseline  0.13    -0.58 0.01
## age_Y1         0.07    -1.27 0.08
## pub_Y1         0.09    -0.76 0.01
## pubt_Y1       -0.04    -0.38 0.01
## age_Y2         0.11    -0.93 0.08
## pub_Y2        -0.17    -0.73 0.01
## pubt_Y2       -0.28     0.11 0.01
## age_Y3         0.07    -1.27 0.08
## pub_Y3        -0.52    -0.27 0.01
## pubt_Y3       -0.46     0.55 0.01

# Create four-panel histogram
library(ggplot2)

# Combine all pub variables pubo a single column
all_pub <- c(data_frame$pub_Baseline, data_frame$pub_Y1, data_frame$pub_Y2, data_frame$pub_Y3)

# Create a data frame with the combined pub values
combined_data <- data.frame(pub = all_pub, Timepopub = rep(c("Baseline", "Y1", "Y2", "Y3"), each = nrow(data_frame)))

# Create the combined histogram with APA-style formatting
ggplot(combined_data, aes(x = pub)) +
  geom_histogram(binwidth = 1, fill = "#0072B2", color = "#0072B2", alpha = 0.7) +
  labs(title = "Histogram of Combined pub", x = "pub", y = "Frequency") +
  facet_wrap(~ Timepopub, scales = "free_x", nrow = 2) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        panel.border = element_rect(color = "black", fill = NA),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        strip.text = element_text(size = 12),
        plot.title = element_text(size = 14, hjust = 0.5),
        strip.background = element_rect(fill = "#E5E5E5"),
        legend.position = "none")

## Warning: Removed 11158 rows containing non-finite values (`stat_bin()`).

################################################################################
# install.packages("corrplot")
library(corrplot)
library(dplyr)
library(ggplot2)
library(reshape2)  

# Select the pub variables
pub_variables <- c("pub_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Subset the data for the selected pub variables
pub_data <- data_frame %>%
  select(all_of(pub_variables))

# Compute the correlation matrix
cor_matrix <- cor(pub_data, use = "complete.obs")
cor_matrix

##              pub_Baseline    pub_Y1    pub_Y2    pub_Y3
## pub_Baseline    1.0000000 0.4450122 0.3553012 0.2729983
## pub_Y1          0.4450122 1.0000000 0.6236506 0.5228071
## pub_Y2          0.3553012 0.6236506 1.0000000 0.6822757
## pub_Y3          0.2729983 0.5228071 0.6822757 1.0000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 4) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

################################################################################

# Convert to long to examine trajectories
library(tidyr)

# Subset 
long_data <- data_frame[, c("IID", "pub_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")]

library(reshape2)

# Convert wide data to long format using melt()
long_data <- melt(data_frame, id.vars = "IID", measure.vars = c("pub_Baseline", "pub_Y1", "pub_Y2", "pub_Y3"),
                  variable.name = "Timepopub", value.name = "pub")

# Sort the long-format data by IID
sorted_long_data <- long_data %>%
  arrange(IID)

# Print the long-format data
# print(long_data)

library(dplyr)
library(ggplot2)

# Randomly select 1000 unique IIDs
unique_iids <- sorted_long_data %>%
  distinct(IID) %>%
  sample_n(500)  # Select 1000 random IIDs

# Subset the data based on the selected IIDs
subset_data <- sorted_long_data %>%
  filter(IID %in% unique_iids$IID)

# Create a longitudinal plot of pub across timepopubs
ggplot(subset_data, aes(x = Timepopub, y = pub, group = IID, color = IID)) +
  geom_line(size = 1) +
  labs(title = "Longitudinal Plot of pub Across Time (Subset)", x = "Timepoint", y = "pub") +
  theme_minimal() +
  theme(legend.position = "none",
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_rect(color = "black", fill = NA),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        plot.title = element_text(size = 14, hjust = 0.5))

## Warning: Removed 307 rows containing missing values (`geom_line()`).

Covariates

library(psych)
# Load parent psychopathology covariate data 
abcl <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/mental-health/mh_p_abcl.csv", header = TRUE, sep = ",", dec = ".")
asr <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/mental-health/mh_p_asr.csv", header = TRUE, sep = ",", dec = ".")
# View(abcl)
# View(asr)

# Remove first row of Identifiers so we are left with only the data:
abcl.data <- abcl[-1,]
asr.data <- asr[-1,]

# Rename subject ID
abcl.data$IID  <- abcl.data[,"src_subject_id"]
asr.data$IID  <- asr.data[,"src_subject_id"]

# Create Y2 assessment data sets for parent psychopathology (Other Parent)
Y2.abcl<-abcl.data[abcl.data$eventname=="2_year_follow_up_y_arm_1",]

# Create 0, 2 assessment data sets for parent psychopathology (Self report)
Baseline.asr<-asr.data[asr.data$eventname=="baseline_year_1_arm_1",]
Y2.asr<-asr.data[asr.data$eventname=="2_year_follow_up_y_arm_1",]

# Rename variables for merge
Baseline.asr$asr_scr_internal_r_b <- Baseline.asr$asr_scr_internal_r
Y2.asr$asr_scr_internal_r_2 <- Y2.asr$asr_scr_internal_r

# Merge 0, 2 assessment data parent psychopathology (Self report)
Merged.asr_Baseline_Y2 <- merge(Baseline.asr, Y2.asr, by = "IID")

# Calculate correlation
correlation <- cor(Merged.asr_Baseline_Y2$asr_scr_internal_r_b, Merged.asr_Baseline_Y2$asr_scr_internal_r_2, use = "pairwise.complete.obs")
print(correlation)

## [1] 0.6915181

library(data.table)
# Keep subset for merge
variables_to_keep <- c("IID","asr_scr_internal_r_b","asr_scr_internal_r_2")

# Convert the data frame to a data.table
setDT(Merged.asr_Baseline_Y2)

# Subset the data table and create a new data table
Merged.asr_Baseline_Y2_subset <- Merged.asr_Baseline_Y2[, ..variables_to_keep]

# Create average asr variable
Merged.asr_Baseline_Y2_subset[, asr_int_ave := (asr_scr_internal_r_b + asr_scr_internal_r_2) / 2]

# Keep subset for acbl data
variables_to_keep <- c("IID","abcl_scr_prob_internal_r")

# Convert the data frame to a data.table
setDT(Y2.abcl)

# Subset the data table and create a new data table
Y2.abcl_subset <- Y2.abcl[, ..variables_to_keep]

# Merge asr abcl data
Merged.asr_abcl <- merge(Merged.asr_Baseline_Y2_subset, Y2.abcl_subset, by = "IID")

# Average together averaged parent internalizing self report with report on other parent
Merged.asr_abcl[, int_p_ave := (asr_int_ave + abcl_scr_prob_internal_r) / 2]

# Descriptive statistics

# Calculate correlation
correlation <- cor(Merged.asr_abcl$asr_int_ave, Merged.asr_abcl$abcl_scr_prob_internal_r, use = "pairwise.complete.obs")
print(correlation)

## [1] 0.4193454

famc <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/culture-environment/ce_p_fes.csv", header = TRUE, sep = ",", dec = ".")

#View(famc)
describe(famc$fes_p_ss_fc) 

##    vars     n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 48733 2.43 1.94      2    2.25 1.48   0   9     9  0.7    -0.07 0.01

summary(famc$fes_p_ss_fc)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   1.000   2.000   2.429   4.000   9.000     418

#Create key for Identifiers:
famc.varlabels <- famc[1,]

#Remove first row of Identifiers so we are left with only the data:
famc.data <- famc[-1,]

#Rename subject ID
famc.data$IID  <- famc.data[,"src_subject_id"]

#Create 0, 1, 2,3 assessment data sets
Baseline.famc<-famc.data[famc.data$eventname=="baseline_year_1_arm_1",]
Y1.famc<-famc.data[famc.data$eventname=="1_year_follow_up_y_arm_1",]
Y2.famc<-famc.data[famc.data$eventname=="2_year_follow_up_y_arm_1",]
Y3.famc<-famc.data[famc.data$eventname=="3_year_follow_up_y_arm_1",]

# Rename variables for merge
Baseline.famc$fes_p_ss_fc_b <- Baseline.famc$fes_p_ss_fc
Y1.famc$fes_p_ss_fc_1 <- Y1.famc$fes_p_ss_fc
Y2.famc$fes_p_ss_fc_2 <- Y2.famc$fes_p_ss_fc
Y3.famc$fes_p_ss_fc_3 <- Y3.famc$fes_p_ss_fc

# Merge all family conflict data sets together
library(data.table)

# List of datasets to merge
famc_datasets <- list(Baseline.famc, Y1.famc, Y2.famc, Y3.famc)

# Merge all data.tables using full outer join based on IID
famc_merged_data <- Reduce(function(x, y) merge(x, y, by = "IID", all = TRUE), famc_datasets)

## Warning in merge.data.frame(x, y, by = "IID", all = TRUE): column names
## 'src_subject_id.x', 'eventname.x', 'fam_enviro1_p.x', 'fam_enviro2r_p.x',
## 'fam_enviro3_p.x', 'fam_enviro4r_p.x', 'fam_enviro5_p.x', 'fam_enviro6_p.x',
## 'fam_enviro7r_p.x', 'fam_enviro8_p.x', 'fam_enviro9r_p.x',
## 'fam_enviro_select_language___1.x', 'fes_16r_p.x', 'fes_17_p.x', 'fes_19_p.x',
## 'fes_21_p.x', 'fes_22_p.x', 'fes_26_p.x', 'fes_27r_p.x', 'fes_29r_p.x',
## 'fes_31_p.x', 'fes_32_p.x', 'fes_36r_p.x', 'fes_37_p.x', 'fes_39_p.x',
## 'fes_41r_p.x', 'fes_42_p.x', 'fes_46r_p.x', 'fes_47_p.x', 'fes_49r_p.x',
## 'fes_51_p.x', 'fes_52r_p.x', 'fes_1_p.x', 'fes_56_p.x', 'fes_57r_p.x',
## 'fes_59_p.x', 'fes_61r_p.x', 'fes_62_p.x', 'fes_66_p.x', 'fes_67_p.x',
## 'fes_69_p.x', 'fes_71_p.x', 'fes_72r_p.x', 'fes_2r_p.x', 'fes_76r_p.x',
## 'fes_77_p.x', 'fes_79r_p.x', 'fes_81_p.x', 'fes_82_p.x', 'fes_86_p.x',
## 'fes_87r_p.x', 'fes_89_p.x', 'fes_6_p.x', 'fes_7r_p.x', 'fes_9_p.x',
## 'fes_11r_p.x', 'fes_12_p.x', 'fes_p_ss_fc.x', 'fes_p_ss_fc_na.x',
## 'fes_p_ss_fc_pr.x', 'fes_p_ss_fc_nm.x', 'fes_p_ss_fc_nt.x',
## 'fes_p_ss_exp_sum_nt.x', 'fes_p_ss_exp_sum_na.x', 'fes_p_ss_exp_sum_pr.x',
## 'fes_p_ss_int_cult_sum.x', 'fes_p_ss_int_cult_sum_nm.x',
## 'fes_p_ss_int_cult_sum_nt.x', 'fes_p_ss_int_cult_sum_na.x',
## 'fes_p_ss_int_cult_sum_pr.x', 'fes_p_ss_act_rec_sum.x',
## 'fes_p_ss_act_rec_sum_nm.x', 'fes_p_ss_act_rec_sum_nt.x',
## 'fes_p_ss_act_rec_sum_na.x', 'fes_p_ss_act_rec_sum_pr.x', 'fes_p_ss_org_sum.x',
## 'fes_p_ss_org_sum_nm.x', 'fes_p_ss_org_sum_nt.x', 'fes_p_ss_org_sum_na.x',
## 'fes_p_ss_org_sum_pr.x', 'fes_p_ss_cohesion_sum.x',
## 'fes_p_ss_cohesion_sum_nm.x', 'fes_p_ss_cohesion_sum_nt.x',
## 'fes_p_ss_cohesion_sum_na.x', 'fes_p_ss_cohesion_sum_pr.x',
## 'fes_p_ss_exp_sum.x', 'fes_p_ss_exp_sum_nm.x', 'src_subject_id.y',
## 'eventname.y', 'fam_enviro1_p.y', 'fam_enviro2r_p.y', 'fam_enviro3_p.y',
## 'fam_enviro4r_p.y', 'fam_enviro5_p.y', 'fam_enviro6_p.y', 'fam_enviro7r_p.y',
## 'fam_enviro8_p.y', 'fam_enviro9r_p.y', 'fam_enviro_select_language___1.y',
## 'fes_16r_p.y', 'fes_17_p.y', 'fes_19_p.y', 'fes_21_p.y', 'fes_22_p.y',
## 'fes_26_p.y', 'fes_27r_p.y', 'fes_29r_p.y', 'fes_31_p.y', 'fes_32_p.y',
## 'fes_36r_p.y', 'fes_37_p.y', 'fes_39_p.y', 'fes_41r_p.y', 'fes_42_p.y',
## 'fes_46r_p.y', 'fes_47_p.y', 'fes_49r_p.y', 'fes_51_p.y', 'fes_52r_p.y',
## 'fes_1_p.y', 'fes_56_p.y', 'fes_57r_p.y', 'fes_59_p.y', 'fes_61r_p.y',
## 'fes_62_p.y', 'fes_66_p.y', 'fes_67_p.y', 'fes_69_p.y', 'fes_71_p.y',
## 'fes_72r_p.y', 'fes_2r_p.y', 'fes_76r_p.y', 'fes_77_p.y', 'fes_79r_p.y',
## 'fes_81_p.y', 'fes_82_p.y', 'fes_86_p.y', 'fes_87r_p.y', 'fes_89_p.y',
## 'fes_6_p.y', 'fes_7r_p.y', 'fes_9_p.y', 'fes_11r_p.y', 'fes_12_p.y',
## 'fes_p_ss_fc.y', 'fes_p_ss_fc_na.y', 'fes_p_ss_fc_pr.y', 'fes_p_ss_fc_nm.y',
## 'fes_p_ss_fc_nt.y', 'fes_p_ss_exp_sum_nt.y', 'fes_p_ss_exp_sum_na.y',
## 'fes_p_ss_exp_sum_pr.y', 'fes_p_ss_int_cult_sum.y',
## 'fes_p_ss_int_cult_sum_nm.y', 'fes_p_ss_int_cult_sum_nt.y',
## 'fes_p_ss_int_cult_sum_na.y', 'fes_p_ss_int_cult_sum_pr.y',
## 'fes_p_ss_act_rec_sum.y', 'fes_p_ss_act_rec_sum_nm.y',
## 'fes_p_ss_act_rec_sum_nt.y', 'fes_p_ss_act_rec_sum_na.y',
## 'fes_p_ss_act_rec_sum_pr.y', 'fes_p_ss_org_sum.y', 'fes_p_ss_org_sum_nm.y',
## 'fes_p_ss_org_sum_nt.y', 'fes_p_ss_org_sum_na.y', 'fes_p_ss_org_sum_pr.y',
## 'fes_p_ss_cohesion_sum.y', 'fes_p_ss_cohesion_sum_nm.y',
## 'fes_p_ss_cohesion_sum_nt.y', 'fes_p_ss_cohesion_sum_na.y',
## 'fes_p_ss_cohesion_sum_pr.y', 'fes_p_ss_exp_sum.y', 'fes_p_ss_exp_sum_nm.y' are
## duplicated in the result

# Select the pub variables
famc_variables <- c("fes_p_ss_fc_b","fes_p_ss_fc_1", "fes_p_ss_fc_2", "fes_p_ss_fc_3")

# Subset the data for the selected pub variables
famc_data_corr <- famc_merged_data %>%
  select(all_of(famc_variables))

# Compute the correlation matrix
cor_matrix <- cor(famc_data_corr, use = "pairwise.complete.obs")
cor_matrix

##               fes_p_ss_fc_b fes_p_ss_fc_1 fes_p_ss_fc_2 fes_p_ss_fc_3
## fes_p_ss_fc_b     1.0000000     0.5759198     0.5667544     0.5339295
## fes_p_ss_fc_1     0.5759198     1.0000000     0.5981592     0.5789034
## fes_p_ss_fc_2     0.5667544     0.5981592     1.0000000     0.6635484
## fes_p_ss_fc_3     0.5339295     0.5789034     0.6635484     1.0000000

# Keep subset for merge
variables_to_keep <- c("IID","fes_p_ss_fc_b","fes_p_ss_fc_1", "fes_p_ss_fc_2", "fes_p_ss_fc_3")

# Convert the data frame to a data.table
setDT(famc_merged_data)

# Subset the data table and create a new data table
famc_merged_data_subset <- famc_merged_data[, ..variables_to_keep]

# Merge family conflict together across waves
famc_merged_data_subset[, famc_ave := rowSums(.SD, na.rm = TRUE) / 4, .SDcols = c("fes_p_ss_fc_b", "fes_p_ss_fc_1", "fes_p_ss_fc_2", "fes_p_ss_fc_3")]

# Keep subset for merge
variables_to_keep <- c("IID","famc_ave")

# Subset the data table and create a new data table
famc_merged_data_subset <- famc_merged_data_subset[, ..variables_to_keep]

# Child specific covariates

# Birth weight
birth <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/physical-health/ph_p_dhx.csv", header = TRUE, sep = ",", dec = ".")

# Delete cases where 'eventname' is "4_year_follow_up_y_arm_1"
birth_baseline <- birth[birth$eventname != "4_year_follow_up_y_arm_1", ]

#Create key for Identifiers:
birth.varlabels <- birth_baseline[1,]

#Remove first row of Identifiers so we are left with only the data:
birth_baseline <- birth_baseline[-1,]

#Rename subject ID
birth_baseline$IID  <- birth_baseline[,"src_subject_id"]

# Keep subset for merge
variables_to_keep <- c("IID","birth_weight_lbs","birth_weight_oz", "devhx_3_p", "devhx_9_alchohol_avg", "devhx_9_alcohol", "devhx_9_cigs_per_day", "devhx_9_tobacco", "devhx_9_marijuana_amt", "devhx_9_marijuana")

# Convert the data frame to a data.table
setDT(birth_baseline)

# Subset the data table and create a new data table
birth.data_subset <- birth_baseline[, ..variables_to_keep]

# Convert ounces to pounds (1 lb = 16 oz) and create birth.data weight variable
birth.data_subset$bw_lbs <- birth.data_subset$birth_weight_lbs + birth.data_subset$birth_weight_oz / 16
describe(birth.data_subset$bw_lbs)

##    vars     n mean   sd median trimmed  mad  min   max range  skew kurtosis
## X1    1 10622 7.02 1.47   7.19    7.07 1.39 1.81 14.75 12.94 -0.29     0.32
##      se
## X1 0.01

hist(birth.data_subset$bw_lbs, 
     main = "Histogram of birth.data Weight", # Title of the histogram
     xlab = "Value",                     # Label for the x-axis
     ylab = "Frequency",                 # Label for the y-axis
     col = "blue",                       # Color of the bars
     border = "black",                   # Color of the bar borders
     breaks = 5)   

# Maternal age 
birth.data_subset$matage <- birth.data_subset$devhx_3_p
describe(birth.data_subset$matage)

##    vars     n  mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 11603 29.39 6.27     30   29.39 5.93  13  60    47 0.02    -0.42 0.06

hist(birth.data_subset$matage, 
     main = "Histogram of Maternal Age", # Title of the histogram
     xlab = "Value",                     # Label for the x-axis
     ylab = "Frequency",                 # Label for the y-axis
     col = "blue",                       # Color of the bars
     border = "black",                   # Color of the bar borders
     breaks = 10) 

# Alcohol use
birth.data_subset$devhx_9_alchohol_avg <- ifelse(birth.data_subset$devhx_9_alcohol == 0, 0,
                                     ifelse(birth.data_subset$devhx_9_alcohol == 999, NA,
                                     no = birth.data_subset$devhx_9_alchohol_avg))

birth.data_subset$matalc_ave <- birth.data_subset$devhx_9_alchohol_avg
describe(birth.data_subset$matalc_ave)

##    vars     n mean   sd median trimmed mad min max range  skew kurtosis   se
## X1    1 11506 0.05 1.01      0       0   0   0  60    60 42.79     2171 0.01

freq_devhx_9_alchohol_avg <- table(birth.data_subset$devhx_9_alchohol_avg)
print(freq_devhx_9_alchohol_avg)

## 
##     0 0.025 0.045  0.05   0.1   0.2  0.25   0.5   0.6     1     2     3     4 
## 11316     1     1     1     4     1     5     9     1    90    32    16     7 
##     5     6     7     8    10    15    18    20    21    50    60 
##     2     2     4     1     5     1     1     1     2     2     1

hist(birth.data_subset$matalc_ave, 
     main = "Histogram of Average Drinks Per Week",  # Title of the histogram
     xlab = "Value",                     # Label for the x-axis
     ylab = "Frequency",                 # Label for the y-axis
     col = "blue",                       # Color of the bars
     border = "black",                   # Color of the bar borders
     breaks = 10)

# Cigarette use

# Recode devhx_9_cigs_per_day
birth.data_subset$devhx_9_cigs_per_day <- ifelse(birth.data_subset$devhx_9_tobacco == 0, 0,
                                     ifelse(birth.data_subset$devhx_9_tobacco == 999, NA,
                                     no = birth.data_subset$devhx_9_cigs_per_day))

birth.data_subset$matcig_ave <- birth.data_subset$devhx_9_cigs_per_day
describe(birth.data_subset$matcig_ave)

##    vars     n mean   sd median trimmed mad min max range skew kurtosis   se
## X1    1 11491 0.33 1.97      0       0   0   0  30    30 7.85    72.71 0.02

hist(birth.data_subset$matcig_ave, 
     main = "Histogram of Average Cigarette Use Per Day",  # Title of the histogram
     xlab = "Value",                     # Label for the x-axis
     ylab = "Frequency",                 # Label for the y-axis
     col = "blue",                       # Color of the bars
     border = "black",                   # Color of the bar borders
     breaks = 10)

# Marijuana
birth.data_subset$devhx_9_marijuana_amt <- ifelse(birth.data_subset$devhx_9_marijuana == 0, 0,
                                     ifelse(birth.data_subset$devhx_9_marijuana == 999, NA,
                                     no = birth.data_subset$devhx_9_marijuana_amt))

birth.data_subset$matmar_ave <- birth.data_subset$devhx_9_marijuana_amt
describe(birth.data_subset$matmar_ave)

##    vars     n mean   sd median trimmed mad min max range  skew kurtosis se
## X1    1 11496 0.03 0.26      0       0   0   0   8     8 13.69   237.81  0

hist(birth.data_subset$matmar_ave, 
     main = "Histogram of Average Marijuana Use Per Day",  # Title of the histogram
     xlab = "Value",                     # Label for the x-axis
     ylab = "Frequency",                 # Label for the y-axis
     col = "blue",                       # Color of the bars
     border = "black",                   # Color of the bar borders
     breaks = 10)

# General socioeconomic status latent factor
ses <- read.csv("C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Data/abcd-data-release-5.1/core/abcd-general/abcd_y_lf.csv", header = TRUE, sep = ",", dec = ".")

#Create key for Identifiers:
ses.varlabels <- ses[1,]

#Remove first row of Identifiers so we are left with only the data:
ses.data <- ses[-1,]

#Rename subject ID
ses.data$IID  <- ses.data[,"src_subject_id"]

# Keep subset for merge
variables_to_keep <- c("IID","latent_factor_ss_general_ses")

# Convert the data frame to a data.table
setDT(ses.data)

# Subset the data table and create a new data table
ses.data_subset <- ses.data[, ..variables_to_keep]

ses.data_subset$ses_lt <- ses.data_subset$latent_factor_ss_general_ses

describe(ses.data_subset$ses_lt)

##    vars    n mean   sd median trimmed  mad   min  max range  skew kurtosis   se
## X1    1 8150    0 0.94   0.26    0.12 0.76 -3.94 1.69  5.62 -1.22     1.33 0.01

hist(ses.data_subset$ses_lt, 
     main = "Histogram of SES Latent Factor Score",  # Title of the histogram
     xlab = "Value",                     # Label for the x-axis
     ylab = "Frequency",                 # Label for the y-axis
     col = "blue",                       # Color of the bars
     border = "black",                   # Color of the bar borders
     breaks = 10)   

################### Merge all covariate data sets together  ####################
library(data.table)

# List of datasets to merge
cov_datasets <- list(Merged.asr_abcl, famc_merged_data_subset, birth.data_subset, ses.data_subset)

# Merge all data.tables using full outer join based on IID
cov_merged_data <- Reduce(function(x, y) merge(x, y, by = "IID", all = TRUE), cov_datasets)

Merge

# Merge all constructed datasets for each phenotype together
library(data.table)

# Drop redundant age variables before merge
library(dplyr)

# List of variables to drop
variables_to_drop <- c("age_Baseline", "age_Y1", "age_Y2", "age_Y3")

# Drop the specified variables from the wchr dataset
wchr_merged_data <- wchr_merged_data %>%
  select(-all_of(variables_to_drop))

# Drop the specified variables from the puberty dataset
pub_merged_data <- pub_merged_data %>%
  select(-all_of(variables_to_drop))

# List of datasets to merge
all_datasets <- list(int_merged_data, wchr_merged_data, pub_merged_data, cov_merged_data, Baseline.demo)

# Merge all data.tables on IID
all_merged <- Reduce(function(x, y) merge(x, y, by = "IID", all = TRUE), all_datasets)

# Find duplicate IDs
# duplicate_ids <- all_merged$IID[duplicated(all_merged$IID)]
# Display the duplicate IDs
# print(duplicate_ids)

Associations (Whole Sample)

# install.packages("Hmisc")
# library("Hmisc")
library("psych")

# Examining cross phenotype associations

# Select the variables to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3",
                           "age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")

# Convert data.table to data frame
data_frame <- as.data.frame(all_merged)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars     n   mean   sd median trimmed   mad    min    max range
## age_Baseline      1 10360 118.97 7.49 119.00  118.87 10.38 107.00 133.00 26.00
## int_Baseline      2 10358   1.03 1.70   0.00    0.64  0.00   0.00  15.00 15.00
## intt_Baseline     3 10355   0.00 1.70  -0.91   -0.37  0.34  -1.16  13.91 15.08
## age_Y1            4  9784 131.08 7.72 131.00  130.99 10.38 117.00 149.00 32.00
## int_Y1            5  9783   1.11 1.78   0.00    0.71  0.00   0.00  14.00 14.00
## intt_Y1           6  9780   0.00 1.77  -0.99   -0.38  0.36  -1.30  12.91 14.21
## age_Y2            7  9523 144.28 8.01 144.00  144.18 10.38 127.00 168.00 41.00
## int_Y2            8  9522   1.23 1.96   0.00    0.79  0.00   0.00  16.00 16.00
## intt_Y2           9  9519   0.00 1.96  -1.02   -0.42  0.63  -1.70  15.03 16.73
## age_Y3           10  8825 154.93 7.77 155.00  154.83 10.38 137.00 175.00 38.00
## int_Y3           11  8821   1.44 2.15   1.00    0.97  1.48   0.00  15.00 15.00
## intt_Y3          12  8819   0.00 2.15  -0.67   -0.44  1.18  -1.82  13.69 15.52
## age_Baseline.1   13 10360 118.97 7.49 119.00  118.87 10.38 107.00 133.00 26.00
## wchr_Baseline    14 10345   0.48 0.07   0.47    0.47  0.06   0.24   1.37  1.13
## wchrt_Baseline   15 10342   0.00 0.07  -0.01   -0.01  0.06  -0.24   0.89  1.13
## age_Y1.1         16  9784 131.08 7.72 131.00  130.99 10.38 117.00 149.00 32.00
## wchr_Y1          17  9714   0.48 0.08   0.47    0.47  0.06   0.27   1.47  1.21
## wchrt_Y1         18  9711   0.00 0.08  -0.02   -0.01  0.06  -0.21   1.00  1.21
## age_Y2.1         19  9523 144.28 8.01 144.00  144.18 10.38 127.00 168.00 41.00
## wchr_Y2          20  7919   0.48 0.08   0.46    0.47  0.07   0.26   1.41  1.15
## wchrt_Y2         21  7917   0.00 0.08  -0.02   -0.01  0.07  -0.22   0.92  1.14
## age_Y3.1         22  8825 154.93 7.77 155.00  154.83 10.38 137.00 175.00 38.00
## wchr_Y3          23  1755   0.49 0.09   0.47    0.48  0.07   0.34   1.26  0.92
## wchrt_Y3         24  1754   0.00 0.08  -0.02   -0.01  0.07  -0.15   0.77  0.92
## age_Baseline.2   25 10360 118.97 7.49 119.00  118.87 10.38 107.00 133.00 26.00
## pub_Baseline     26  8397   2.08 0.83   2.00    2.06  1.48   1.00   5.00  4.00
## pubt_Baseline    27  8363   0.00 0.81   0.05   -0.01  1.05  -1.61   3.08  4.69
## age_Y1.2         28  9784 131.08 7.72 131.00  130.99 10.38 117.00 149.00 32.00
## pub_Y1           29  4247   2.27 0.90   2.00    2.25  1.48   1.00   5.00  4.00
## pubt_Y1          30  4224   0.00 0.80   0.04    0.00  0.95  -2.12   3.08  5.21
## age_Y2.2         31  9523 144.28 8.01 144.00  144.18 10.38 127.00 168.00 41.00
## pub_Y2           32  9067   2.69 0.97   3.00    2.73  1.48   1.00   5.00  4.00
## pubt_Y2          33  9064   0.00 0.77   0.04    0.02  0.75  -2.84   3.02  5.86
## age_Y3.2         34  8825 154.93 7.77 155.00  154.83 10.38 137.00 175.00 38.00
## pub_Y3           35  8595   3.12 0.93   3.00    3.20  1.48   1.00   5.00  4.00
## pubt_Y3          36  8592   0.00 0.74   0.11    0.03  0.69  -2.94   2.53  5.47
## int_p_ave        37  9202   7.71 6.17   6.00    6.85  5.19   0.00  48.50 48.50
## famc_ave         38 11868   2.26 1.58   2.00    2.12  1.48   0.00   8.75  8.75
## bw_lbs           39 10622   7.02 1.47   7.19    7.07  1.39   1.81  14.75 12.94
## matage           40 11603  29.39 6.27  30.00   29.39  5.93  13.00  60.00 47.00
## matalc_ave       41 11506   0.05 1.01   0.00    0.00  0.00   0.00  60.00 60.00
## matcig_ave       42 11491   0.33 1.97   0.00    0.00  0.00   0.00  30.00 30.00
## matmar_ave       43 11496   0.03 0.26   0.00    0.00  0.00   0.00   8.00  8.00
## ses_lt           44  8150   0.00 0.94   0.26    0.12  0.76  -3.94   1.69  5.62
##                 skew kurtosis   se
## age_Baseline    0.07    -1.26 0.07
## int_Baseline    2.52     8.16 0.02
## intt_Baseline   2.51     8.15 0.02
## age_Y1          0.07    -1.18 0.08
## int_Y1          2.42     7.28 0.02
## intt_Y1         2.42     7.26 0.02
## age_Y2          0.11    -0.93 0.08
## int_Y2          2.38     7.12 0.02
## intt_Y2         2.36     7.07 0.02
## age_Y3          0.09    -1.02 0.08
## int_Y3          2.14     5.47 0.02
## intt_Y3         2.12     5.38 0.02
## age_Baseline.1  0.07    -1.26 0.07
## wchr_Baseline   1.31     4.92 0.00
## wchrt_Baseline  1.31     4.92 0.00
## age_Y1.1        0.07    -1.18 0.08
## wchr_Y1         2.05    13.96 0.00
## wchrt_Y1        2.05    13.98 0.00
## age_Y2.1        0.11    -0.93 0.08
## wchr_Y2         1.52     6.84 0.00
## wchrt_Y2        1.52     6.77 0.00
## age_Y3.1        0.09    -1.02 0.08
## wchr_Y3         1.72     7.24 0.00
## wchrt_Y3        1.72     7.30 0.00
## age_Baseline.2  0.07    -1.26 0.07
## pub_Baseline    0.19    -0.75 0.01
## pubt_Baseline   0.13    -0.58 0.01
## age_Y1.2        0.07    -1.18 0.08
## pub_Y1          0.09    -0.76 0.01
## pubt_Y1        -0.04    -0.38 0.01
## age_Y2.2        0.11    -0.93 0.08
## pub_Y2         -0.17    -0.73 0.01
## pubt_Y2        -0.28     0.11 0.01
## age_Y3.2        0.09    -1.02 0.08
## pub_Y3         -0.52    -0.27 0.01
## pubt_Y3        -0.46     0.55 0.01
## int_p_ave       1.40     2.38 0.06
## famc_ave        0.79     0.28 0.01
## bw_lbs         -0.29     0.32 0.01
## matage          0.02    -0.42 0.06
## matalc_ave     42.79  2171.00 0.01
## matcig_ave      7.85    72.71 0.02
## matmar_ave     13.69   237.81 0.00
## ses_lt         -1.22     1.33 0.01

# Select the variables
all_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3","int_Baseline", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3","pubt_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Select the variables for age regressed
allt_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3")

# Subset the data for the selected variables
all_data <- data_frame %>%
  select(all_of(all_variables))

# Subset the data for the selected t variables
allt_data <- data_frame %>%
  select(all_of(allt_variables))

# Compute the correlation matrix for raw vars
cor_matrix <- cor(all_data, use = "pairwise.complete.obs")
cor_matrix

##               int_Baseline      int_Y1     int_Y2     int_Y3 wchr_Baseline
## int_Baseline   1.000000000 0.630956838 0.53983486 0.46201264    0.09421033
## int_Y1         0.630956838 1.000000000 0.61654564 0.54822161    0.10997044
## int_Y2         0.539834859 0.616545644 1.00000000 0.63135150    0.08641891
## int_Y3         0.462012636 0.548221610 0.63135150 1.00000000    0.08709353
## wchr_Baseline  0.094210334 0.109970439 0.08641891 0.08709353    1.00000000
## wchr_Y1        0.082155429 0.097856727 0.07732259 0.08014528    0.71680624
## wchr_Y2        0.092845659 0.104111508 0.09641904 0.09949183    0.69831350
## wchr_Y3        0.109665239 0.096286181 0.10456406 0.11794590    0.65697357
## pubt_Baseline  0.045649550 0.041600401 0.04626853 0.05403143    0.11263871
## pub_Y1        -0.006522673 0.001727880 0.04866219 0.08002086    0.09795445
## pub_Y2        -0.007341246 0.013483119 0.05397715 0.07161682    0.10864425
## pub_Y3        -0.019332393 0.002501385 0.03781863 0.08179382    0.09660333
##                  wchr_Y1    wchr_Y2    wchr_Y3 pubt_Baseline       pub_Y1
## int_Baseline  0.08215543 0.09284566 0.10966524    0.04564955 -0.006522673
## int_Y1        0.09785673 0.10411151 0.09628618    0.04160040  0.001727880
## int_Y2        0.07732259 0.09641904 0.10456406    0.04626853  0.048662189
## int_Y3        0.08014528 0.09949183 0.11794590    0.05403143  0.080020859
## wchr_Baseline 0.71680624 0.69831350 0.65697357    0.11263871  0.097954455
## wchr_Y1       1.00000000 0.71687773 0.71355018    0.12288615  0.090946935
## wchr_Y2       0.71687773 1.00000000 0.78890862    0.11102490  0.103963494
## wchr_Y3       0.71355018 0.78890862 1.00000000    0.12089002  0.130695829
## pubt_Baseline 0.12288615 0.11102490 0.12089002    1.00000000  0.335130363
## pub_Y1        0.09094694 0.10396349 0.13069583    0.33513036  1.000000000
## pub_Y2        0.07793357 0.07602554 0.12102640    0.21109658  0.619215464
## pub_Y3        0.06772496 0.05964220 0.10013681    0.14508693  0.520463625
##                     pub_Y2       pub_Y3
## int_Baseline  -0.007341246 -0.019332393
## int_Y1         0.013483119  0.002501385
## int_Y2         0.053977146  0.037818628
## int_Y3         0.071616821  0.081793822
## wchr_Baseline  0.108644246  0.096603333
## wchr_Y1        0.077933573  0.067724956
## wchr_Y2        0.076025543  0.059642205
## wchr_Y3        0.121026397  0.100136805
## pubt_Baseline  0.211096582  0.145086928
## pub_Y1         0.619215464  0.520463625
## pub_Y2         1.000000000  0.689156941
## pub_Y3         0.689156941  1.000000000

# Compute the correlation matrix for age regressed vars
cor_matrix_t <- cor(allt_data, use = "pairwise.complete.obs")
cor_matrix_t

##                intt_Baseline    intt_Y1    intt_Y2    intt_Y3 wchrt_Baseline
## intt_Baseline     1.00000000 0.63064547 0.54124862 0.46623642     0.09420546
## intt_Y1           0.63064547 1.00000000 0.61664321 0.54982975     0.11025942
## intt_Y2           0.54124862 0.61664321 1.00000000 0.63225262     0.08747187
## intt_Y3           0.46623642 0.54982975 0.63225262 1.00000000     0.08760491
## wchrt_Baseline    0.09420546 0.11025942 0.08747187 0.08760491     1.00000000
## wchrt_Y1          0.08176716 0.09823265 0.07972661 0.08159648     0.71684106
## wchrt_Y2          0.09178623 0.10458623 0.09745399 0.10113100     0.69801814
## wchrt_Y3          0.10955623 0.09625793 0.10486864 0.11529913     0.65824640
## pubt_Baseline     0.04578610 0.04161121 0.04700142 0.05528502     0.11266131
## pubt_Y1           0.02991298 0.02365393 0.05320324 0.07119100     0.12027224
## pubt_Y2           0.02408069 0.02140225 0.04578905 0.05380737     0.14853834
## pubt_Y3           0.01959947 0.01548506 0.03790738 0.06451921     0.13071109
##                  wchrt_Y1   wchrt_Y2   wchrt_Y3 pubt_Baseline    pubt_Y1
## intt_Baseline  0.08176716 0.09178623 0.10955623    0.04578610 0.02991298
## intt_Y1        0.09823265 0.10458623 0.09625793    0.04161121 0.02365393
## intt_Y2        0.07972661 0.09745399 0.10486864    0.04700142 0.05320324
## intt_Y3        0.08159648 0.10113100 0.11529913    0.05528502 0.07119100
## wchrt_Baseline 0.71684106 0.69801814 0.65824640    0.11266131 0.12027224
## wchrt_Y1       1.00000000 0.71660044 0.71515631    0.12299839 0.12462692
## wchrt_Y2       0.71660044 1.00000000 0.78839622    0.11072695 0.13146828
## wchrt_Y3       0.71515631 0.78839622 1.00000000    0.12095920 0.14146887
## pubt_Baseline  0.12299839 0.11072695 0.12095920    1.00000000 0.38587966
## pubt_Y1        0.12462692 0.13146828 0.14146887    0.38587966 1.00000000
## pubt_Y2        0.12407488 0.11678282 0.14725275    0.27067965 0.49622410
## pubt_Y3        0.10888941 0.10147091 0.12343566    0.18965426 0.36424327
##                   pubt_Y2    pubt_Y3
## intt_Baseline  0.02408069 0.01959947
## intt_Y1        0.02140225 0.01548506
## intt_Y2        0.04578905 0.03790738
## intt_Y3        0.05380737 0.06451921
## wchrt_Baseline 0.14853834 0.13071109
## wchrt_Y1       0.12407488 0.10888941
## wchrt_Y2       0.11678282 0.10147091
## wchrt_Y3       0.14725275 0.12343566
## pubt_Baseline  0.27067965 0.18965426
## pubt_Y1        0.49622410 0.36424327
## pubt_Y2        1.00000000 0.51949657
## pubt_Y3        0.51949657 1.00000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Create a ggheatmap for age regressed variables
ggheatmap <- ggplot(melt(cor_matrix_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Correlation matrix with covariates
# Select the variables for age regressed and covariates
allt_cov_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3", "int_p_ave", "famc_ave", "bw_lbs", "matage", "matalc_ave", "matcig_ave", "matmar_ave", "ses_lt")

# Subset the data for the selected t variables
allt_cov_data <- data_frame %>%
  select(all_of(allt_cov_variables))

# Compute the correlation matrix for age regressed vars + covariates
cor_matrix_cov_t <- cor(allt_cov_data, use = "pairwise.complete.obs")
cor_matrix_cov_t

##                intt_Baseline      intt_Y1     intt_Y2     intt_Y3
## intt_Baseline     1.00000000  0.630645473  0.54124862  0.46623642
## intt_Y1           0.63064547  1.000000000  0.61664321  0.54982975
## intt_Y2           0.54124862  0.616643208  1.00000000  0.63225262
## intt_Y3           0.46623642  0.549829749  0.63225262  1.00000000
## wchrt_Baseline    0.09420546  0.110259417  0.08747187  0.08760491
## wchrt_Y1          0.08176716  0.098232649  0.07972661  0.08159648
## wchrt_Y2          0.09178623  0.104586229  0.09745399  0.10113100
## wchrt_Y3          0.10955623  0.096257927  0.10486864  0.11529913
## pubt_Baseline     0.04578610  0.041611215  0.04700142  0.05528502
## pubt_Y1           0.02991298  0.023653930  0.05320324  0.07119100
## pubt_Y2           0.02408069  0.021402251  0.04578905  0.05380737
## pubt_Y3           0.01959947  0.015485063  0.03790738  0.06451921
## int_p_ave         0.37275936  0.375394922  0.42555967  0.36468496
## famc_ave          0.16332523  0.163910352  0.18646043  0.19799013
## bw_lbs            0.00239957  0.020540328  0.02014186  0.04266874
## matage           -0.09619319 -0.064933563 -0.04302733 -0.03271720
## matalc_ave        0.02607338  0.005490829  0.03071013  0.02631768
## matcig_ave        0.06180368  0.079261679  0.06899566  0.07294876
## matmar_ave        0.04767395  0.038943782  0.05110678  0.05030890
## ses_lt           -0.24253285 -0.204770990 -0.17953514 -0.15227664
##                wchrt_Baseline      wchrt_Y1     wchrt_Y2    wchrt_Y3
## intt_Baseline     0.094205455  0.0817671618  0.091786228  0.10955623
## intt_Y1           0.110259417  0.0982326486  0.104586229  0.09625793
## intt_Y2           0.087471867  0.0797266136  0.097453985  0.10486864
## intt_Y3           0.087604910  0.0815964845  0.101130997  0.11529913
## wchrt_Baseline    1.000000000  0.7168410617  0.698018144  0.65824640
## wchrt_Y1          0.716841062  1.0000000000  0.716600444  0.71515631
## wchrt_Y2          0.698018144  0.7166004442  1.000000000  0.78839622
## wchrt_Y3          0.658246397  0.7151563079  0.788396218  1.00000000
## pubt_Baseline     0.112661307  0.1229983865  0.110726948  0.12095920
## pubt_Y1           0.120272245  0.1246269217  0.131468279  0.14146887
## pubt_Y2           0.148538336  0.1240748799  0.116782824  0.14725275
## pubt_Y3           0.130711091  0.1088894123  0.101470910  0.12343566
## int_p_ave         0.040478356  0.0581244791  0.051730479  0.04544840
## famc_ave         -0.011379753 -0.0002494606  0.005091372  0.02619326
## bw_lbs            0.076058866  0.0674241045  0.041641456  0.08870230
## matage           -0.081518900 -0.0898311275 -0.103686013 -0.13210681
## matalc_ave        0.008659337  0.0024405805  0.004639121 -0.02753863
## matcig_ave        0.066930732  0.0597793669  0.073617674  0.15610422
## matmar_ave        0.038093638  0.0464731525  0.049507906  0.01815518
## ses_lt           -0.243731430 -0.2249491987 -0.273176660 -0.26153002
##                pubt_Baseline     pubt_Y1     pubt_Y2       pubt_Y3   int_p_ave
## intt_Baseline    0.045786104  0.02991298  0.02408069  0.0195994650  0.37275936
## intt_Y1          0.041611215  0.02365393  0.02140225  0.0154850631  0.37539492
## intt_Y2          0.047001417  0.05320324  0.04578905  0.0379073753  0.42555967
## intt_Y3          0.055285024  0.07119100  0.05380737  0.0645192122  0.36468496
## wchrt_Baseline   0.112661307  0.12027224  0.14853834  0.1307110912  0.04047836
## wchrt_Y1         0.122998386  0.12462692  0.12407488  0.1088894123  0.05812448
## wchrt_Y2         0.110726948  0.13146828  0.11678282  0.1014709100  0.05173048
## wchrt_Y3         0.120959201  0.14146887  0.14725275  0.1234356635  0.04544840
## pubt_Baseline    1.000000000  0.38587966  0.27067965  0.1896542588  0.03599774
## pubt_Y1          0.385879660  1.00000000  0.49622410  0.3642432680  0.02901371
## pubt_Y2          0.270679647  0.49622410  1.00000000  0.5194965686  0.03884291
## pubt_Y3          0.189654259  0.36424327  0.51949657  1.0000000000  0.03526137
## int_p_ave        0.035997741  0.02901371  0.03884291  0.0352613684  1.00000000
## famc_ave        -0.009152256 -0.02155805 -0.01616332 -0.0305782523  0.32783349
## bw_lbs          -0.015409250  0.00589589 -0.02708632  0.0034639507  0.01603960
## matage          -0.107375368 -0.07173358 -0.09377695 -0.0789720115 -0.06562474
## matalc_ave      -0.006473348  0.01383175  0.01879134  0.0004869273  0.04080926
## matcig_ave       0.030274659  0.04971785  0.03031331  0.0118858166  0.10657556
## matmar_ave       0.027808883  0.05044946  0.02405944  0.0081518004  0.06782937
## ses_lt          -0.177075055 -0.19264180 -0.17437762 -0.1453937375 -0.31987348
##                     famc_ave       bw_lbs       matage    matalc_ave
## intt_Baseline   0.1633252316  0.002399570 -0.096193191  0.0260733750
## intt_Y1         0.1639103521  0.020540328 -0.064933563  0.0054908293
## intt_Y2         0.1864604328  0.020141862 -0.043027330  0.0307101310
## intt_Y3         0.1979901286  0.042668742 -0.032717199  0.0263176845
## wchrt_Baseline -0.0113797530  0.076058866 -0.081518900  0.0086593372
## wchrt_Y1       -0.0002494606  0.067424104 -0.089831127  0.0024405805
## wchrt_Y2        0.0050913717  0.041641456 -0.103686013  0.0046391205
## wchrt_Y3        0.0261932587  0.088702296 -0.132106813 -0.0275386332
## pubt_Baseline  -0.0091522555 -0.015409250 -0.107375368 -0.0064733477
## pubt_Y1        -0.0215580542  0.005895890 -0.071733583  0.0138317451
## pubt_Y2        -0.0161633150 -0.027086321 -0.093776954  0.0187913431
## pubt_Y3        -0.0305782523  0.003463951 -0.078972012  0.0004869273
## int_p_ave       0.3278334852  0.016039604 -0.065624737  0.0408092630
## famc_ave        1.0000000000 -0.004026514  0.019965628  0.0256368853
## bw_lbs         -0.0040265138  1.000000000 -0.004664972 -0.0109385931
## matage          0.0199656281 -0.004664972  1.000000000  0.0220110992
## matalc_ave      0.0256368853 -0.010938593  0.022011099  1.0000000000
## matcig_ave      0.0262981455 -0.048991436 -0.071868552  0.1898145027
## matmar_ave      0.0144338679 -0.006957648 -0.079615410  0.0273110257
## ses_lt         -0.1113415610  0.060106035  0.503106903 -0.0173600688
##                 matcig_ave   matmar_ave      ses_lt
## intt_Baseline   0.06180368  0.047673953 -0.24253285
## intt_Y1         0.07926168  0.038943782 -0.20477099
## intt_Y2         0.06899566  0.051106781 -0.17953514
## intt_Y3         0.07294876  0.050308902 -0.15227664
## wchrt_Baseline  0.06693073  0.038093638 -0.24373143
## wchrt_Y1        0.05977937  0.046473153 -0.22494920
## wchrt_Y2        0.07361767  0.049507906 -0.27317666
## wchrt_Y3        0.15610422  0.018155182 -0.26153002
## pubt_Baseline   0.03027466  0.027808883 -0.17707505
## pubt_Y1         0.04971785  0.050449456 -0.19264180
## pubt_Y2         0.03031331  0.024059436 -0.17437762
## pubt_Y3         0.01188582  0.008151800 -0.14539374
## int_p_ave       0.10657556  0.067829366 -0.31987348
## famc_ave        0.02629815  0.014433868 -0.11134156
## bw_lbs         -0.04899144 -0.006957648  0.06010603
## matage         -0.07186855 -0.079615410  0.50310690
## matalc_ave      0.18981450  0.027311026 -0.01736007
## matcig_ave      1.00000000  0.117620621 -0.21936176
## matmar_ave      0.11762062  1.000000000 -0.15323254
## ses_lt         -0.21936176 -0.153232535  1.00000000

# Create a ggheatmap for age regressed variables + covariates
ggheatmap <- ggplot(melt(cor_matrix_cov_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 2) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Associations (White sample)

# subset data to just White participants
subset_all_merged <- all_merged[all_merged$race3 == 1, ]

# Examining cross phenotype associations

# Select the variables to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3",
                           "age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")

# Convert data.table to data frame
data_frame <- as.data.frame(subset_all_merged)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars    n   mean   sd median trimmed   mad    min    max range
## age_Baseline      1 6170 119.17 7.52 119.00  119.09 10.38 107.00 132.00 25.00
## int_Baseline      2 6168   0.96 1.61   0.00    0.60  0.00   0.00  14.00 14.00
## intt_Baseline     3 6167  -0.06 1.61  -0.92   -0.41  0.33  -1.16  12.92 14.08
## age_Y1            4 5975 131.34 7.75 131.00  131.27 10.38 117.00 149.00 32.00
## int_Y1            5 5975   1.06 1.72   0.00    0.67  0.00   0.00  14.00 14.00
## intt_Y1           6 5974  -0.05 1.72  -0.99   -0.42  0.35  -1.28  12.91 14.19
## age_Y2            7 5831 144.48 8.03 144.00  144.39 10.38 127.00 168.00 41.00
## int_Y2            8 5830   1.21 1.92   0.00    0.78  0.00   0.00  15.00 15.00
## intt_Y2           9 5829  -0.03 1.91  -1.03   -0.43  0.62  -1.70  13.87 15.56
## age_Y3           10 5487 155.16 7.76 155.00  155.07  8.90 137.00 175.00 38.00
## int_Y3           11 5484   1.46 2.15   1.00    0.99  1.48   0.00  15.00 15.00
## intt_Y3          12 5484   0.01 2.14  -0.63   -0.42  1.25  -1.82  13.69 15.52
## age_Baseline.1   13 6170 119.17 7.52 119.00  119.09 10.38 107.00 132.00 25.00
## wchr_Baseline    14 6161   0.47 0.06   0.45    0.46  0.05   0.30   0.81  0.51
## wchrt_Baseline   15 6160  -0.01 0.06  -0.03   -0.02  0.05  -0.18   0.33  0.51
## age_Y1.1         16 5975 131.34 7.75 131.00  131.27 10.38 117.00 149.00 32.00
## wchr_Y1          17 5942   0.47 0.07   0.46    0.46  0.05   0.27   1.42  1.16
## wchrt_Y1         18 5941  -0.01 0.07  -0.03   -0.02  0.05  -0.21   0.94  1.15
## age_Y2.1         19 5831 144.48 8.03 144.00  144.39 10.38 127.00 168.00 41.00
## wchr_Y2          20 5018   0.47 0.07   0.45    0.46  0.06   0.26   1.39  1.13
## wchrt_Y2         21 5017  -0.01 0.07  -0.03   -0.02  0.06  -0.22   0.90  1.12
## age_Y3.1         22 5487 155.16 7.76 155.00  155.07  8.90 137.00 175.00 38.00
## wchr_Y3          23 1114   0.47 0.07   0.46    0.47  0.06   0.34   1.26  0.92
## wchrt_Y3         24 1114  -0.02 0.07  -0.03   -0.02  0.06  -0.15   0.77  0.92
## age_Baseline.2   25 6170 119.17 7.52 119.00  119.09 10.38 107.00 132.00 25.00
## pub_Baseline     26 5107   1.97 0.80   2.00    1.94  1.48   1.00   5.00  4.00
## pubt_Baseline    27 5096  -0.11 0.77   0.04   -0.12  0.98  -1.61   3.04  4.64
## age_Y1.2         28 5975 131.34 7.75 131.00  131.27 10.38 117.00 149.00 32.00
## pub_Y1           29 2900   2.17 0.88   2.00    2.15  1.48   1.00   5.00  4.00
## pubt_Y1          30 2888  -0.10 0.78  -0.01   -0.10  0.89  -2.12   3.08  5.21
## age_Y2.2         31 5831 144.48 8.03 144.00  144.39 10.38 127.00 168.00 41.00
## pub_Y2           32 5628   2.56 0.95   3.00    2.57  1.48   1.00   5.00  4.00
## pubt_Y2          33 5627  -0.13 0.75  -0.11   -0.11  0.74  -2.84   2.85  5.69
## age_Y3.2         34 5487 155.16 7.76 155.00  155.07  8.90 137.00 175.00 38.00
## pub_Y3           35 5410   3.03 0.93   3.00    3.11  1.48   1.00   5.00  4.00
## pubt_Y3          36 5409  -0.09 0.74   0.03   -0.06  0.69  -2.94   2.15  5.09
## int_p_ave        37 5479   7.76 5.96   6.25    6.96  5.19   0.00  48.50 48.50
## famc_ave         38 6172   2.36 1.62   2.00    2.22  1.48   0.00   8.25  8.25
## bw_lbs           39 5731   7.08 1.49   7.25    7.14  1.39   2.19  13.00 10.81
## matage           40 6127  30.85 5.61  31.00   30.88  5.93  14.00  52.00 38.00
## matalc_ave       41 6055   0.05 0.82   0.00    0.00  0.00   0.00  50.00 50.00
## matcig_ave       42 6060   0.35 2.12   0.00    0.00  0.00   0.00  30.00 30.00
## matmar_ave       43 6063   0.02 0.21   0.00    0.00  0.00   0.00   7.00  7.00
## ses_lt           44 4712   0.29 0.75   0.49    0.40  0.52  -3.69   1.63  5.32
##                 skew kurtosis   se
## age_Baseline    0.05    -1.26 0.10
## int_Baseline    2.54     8.65 0.02
## intt_Baseline   2.52     8.60 0.02
## age_Y1          0.05    -1.20 0.10
## int_Y1          2.46     7.57 0.02
## intt_Y1         2.45     7.52 0.02
## age_Y2          0.10    -0.95 0.11
## int_Y2          2.36     7.00 0.03
## intt_Y2         2.34     6.95 0.03
## age_Y3          0.08    -1.04 0.10
## int_Y3          2.12     5.37 0.03
## intt_Y3         2.10     5.26 0.03
## age_Baseline.1  0.05    -1.26 0.10
## wchr_Baseline   1.10     2.02 0.00
## wchrt_Baseline  1.11     2.03 0.00
## age_Y1.1        0.05    -1.20 0.10
## wchr_Y1         2.80    26.15 0.00
## wchrt_Y1        2.80    26.08 0.00
## age_Y2.1        0.10    -0.95 0.11
## wchr_Y2         1.52     8.17 0.00
## wchrt_Y2        1.52     8.05 0.00
## age_Y3.1        0.08    -1.04 0.10
## wchr_Y3         2.13    13.22 0.00
## wchrt_Y3        2.12    13.19 0.00
## age_Baseline.2  0.05    -1.26 0.10
## pub_Baseline    0.24    -0.89 0.01
## pubt_Baseline   0.15    -0.73 0.01
## age_Y1.2        0.05    -1.20 0.10
## pub_Y1          0.13    -0.86 0.02
## pubt_Y1         0.00    -0.38 0.01
## age_Y2.2        0.10    -0.95 0.11
## pub_Y2         -0.10    -0.76 0.01
## pubt_Y2        -0.27     0.05 0.01
## age_Y3.2        0.08    -1.04 0.10
## pub_Y3         -0.44    -0.40 0.01
## pubt_Y3        -0.38     0.29 0.01
## int_p_ave       1.34     2.14 0.08
## famc_ave        0.71     0.05 0.02
## bw_lbs         -0.35     0.05 0.02
## matage         -0.02    -0.22 0.07
## matalc_ave     44.32  2429.18 0.01
## matcig_ave      7.55    63.80 0.03
## matmar_ave     17.56   388.64 0.00
## ses_lt         -1.69     3.74 0.01

# Select the variables
all_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3","int_Baseline", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3","pubt_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Select the variables for age regressed
allt_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3")

# Subset the data for the selected variables
all_data <- data_frame %>%
  select(all_of(all_variables))

# Subset the data for the selected t variables
allt_data <- data_frame %>%
  select(all_of(allt_variables))

# Compute the correlation matrix for raw vars
cor_matrix <- cor(all_data, use = "pairwise.complete.obs")
cor_matrix

##               int_Baseline        int_Y1     int_Y2     int_Y3 wchr_Baseline
## int_Baseline   1.000000000  6.358046e-01 0.55293095 0.47270800    0.11290766
## int_Y1         0.635804561  1.000000e+00 0.62038926 0.56217117    0.12904854
## int_Y2         0.552930949  6.203893e-01 1.00000000 0.64081678    0.11388056
## int_Y3         0.472708000  5.621712e-01 0.64081678 1.00000000    0.11973982
## wchr_Baseline  0.112907662  1.290485e-01 0.11388056 0.11973982    1.00000000
## wchr_Y1        0.088159682  1.041213e-01 0.09291038 0.10307698    0.64768274
## wchr_Y2        0.086590027  1.118501e-01 0.11865753 0.12414427    0.65429254
## wchr_Y3        0.066778899  5.306411e-02 0.10879629 0.12367546    0.60950412
## pubt_Baseline  0.037518749  2.880796e-02 0.04517299 0.06839935    0.09999110
## pub_Y1        -0.013795136 -1.519157e-03 0.06457494 0.08706338    0.10466730
## pub_Y2        -0.009858777  1.992103e-05 0.05092155 0.06922206    0.08847407
## pub_Y3        -0.026797664 -7.357648e-03 0.04091553 0.08512584    0.09503871
##                  wchr_Y1    wchr_Y2    wchr_Y3 pubt_Baseline       pub_Y1
## int_Baseline  0.08815968 0.08659003 0.06677890    0.03751875 -0.013795136
## int_Y1        0.10412135 0.11185006 0.05306411    0.02880796 -0.001519157
## int_Y2        0.09291038 0.11865753 0.10879629    0.04517299  0.064574941
## int_Y3        0.10307698 0.12414427 0.12367546    0.06839935  0.087063377
## wchr_Baseline 0.64768274 0.65429254 0.60950412    0.09999110  0.104667303
## wchr_Y1       1.00000000 0.66436617 0.66503848    0.09621152  0.083977453
## wchr_Y2       0.66436617 1.00000000 0.76424120    0.10361335  0.105749095
## wchr_Y3       0.66503848 0.76424120 1.00000000    0.08066410  0.192016907
## pubt_Baseline 0.09621152 0.10361335 0.08066410    1.00000000  0.300922119
## pub_Y1        0.08397745 0.10574909 0.19201691    0.30092212  1.000000000
## pub_Y2        0.05041293 0.05746137 0.11988357    0.16941885  0.620470593
## pub_Y3        0.05077874 0.04481120 0.09563058    0.10934600  0.527886201
##                      pub_Y2       pub_Y3
## int_Baseline  -9.858777e-03 -0.026797664
## int_Y1         1.992103e-05 -0.007357648
## int_Y2         5.092155e-02  0.040915533
## int_Y3         6.922206e-02  0.085125843
## wchr_Baseline  8.847407e-02  0.095038711
## wchr_Y1        5.041293e-02  0.050778744
## wchr_Y2        5.746137e-02  0.044811204
## wchr_Y3        1.198836e-01  0.095630583
## pubt_Baseline  1.694188e-01  0.109345999
## pub_Y1         6.204706e-01  0.527886201
## pub_Y2         1.000000e+00  0.707960442
## pub_Y3         7.079604e-01  1.000000000

# Compute the correlation matrix for age regressed vars
cor_matrix_t <- cor(allt_data, use = "pairwise.complete.obs")
cor_matrix_t

##                intt_Baseline    intt_Y1    intt_Y2    intt_Y3 wchrt_Baseline
## intt_Baseline     1.00000000 0.63459951 0.55335885 0.47612108     0.11274863
## intt_Y1           0.63459951 1.00000000 0.61992020 0.56421070     0.12888069
## intt_Y2           0.55335885 0.61992020 1.00000000 0.64181976     0.11523869
## intt_Y3           0.47612108 0.56421070 0.64181976 1.00000000     0.12005757
## wchrt_Baseline    0.11274863 0.12888069 0.11523869 0.12005757     1.00000000
## wchrt_Y1          0.08730488 0.10451856 0.09697969 0.10571372     0.64768020
## wchrt_Y2          0.08485624 0.11161811 0.11984600 0.12694736     0.65400281
## wchrt_Y3          0.06787232 0.05496479 0.11039562 0.12093410     0.61119443
## pubt_Baseline     0.03528350 0.02797397 0.04656040 0.07171897     0.09973312
## pubt_Y1           0.03103921 0.02840624 0.06444200 0.08064207     0.12975503
## pubt_Y2           0.02126167 0.01126923 0.04240770 0.05764760     0.12894969
## pubt_Y3           0.00782280 0.01017106 0.04139724 0.07370080     0.13314634
##                  wchrt_Y1   wchrt_Y2   wchrt_Y3 pubt_Baseline    pubt_Y1
## intt_Baseline  0.08730488 0.08485624 0.06787232    0.03528350 0.03103921
## intt_Y1        0.10451856 0.11161811 0.05496479    0.02797397 0.02840624
## intt_Y2        0.09697969 0.11984600 0.11039562    0.04656040 0.06444200
## intt_Y3        0.10571372 0.12694736 0.12093410    0.07171897 0.08064207
## wchrt_Baseline 0.64768020 0.65400281 0.61119443    0.09973312 0.12975503
## wchrt_Y1       1.00000000 0.66408794 0.66740853    0.09586293 0.12909149
## wchrt_Y2       0.66408794 1.00000000 0.76658701    0.10217770 0.14120160
## wchrt_Y3       0.66740853 0.76658701 1.00000000    0.07874789 0.20228954
## pubt_Baseline  0.09586293 0.10217770 0.07874789    1.00000000 0.36851872
## pubt_Y1        0.12909149 0.14120160 0.20228954    0.36851872 1.00000000
## pubt_Y2        0.10501431 0.11444949 0.14590497    0.25344056 0.48920961
## pubt_Y3        0.10611658 0.10424138 0.11103103    0.18049007 0.37453324
##                   pubt_Y2    pubt_Y3
## intt_Baseline  0.02126167 0.00782280
## intt_Y1        0.01126923 0.01017106
## intt_Y2        0.04240770 0.04139724
## intt_Y3        0.05764760 0.07370080
## wchrt_Baseline 0.12894969 0.13314634
## wchrt_Y1       0.10501431 0.10611658
## wchrt_Y2       0.11444949 0.10424138
## wchrt_Y3       0.14590497 0.11103103
## pubt_Baseline  0.25344056 0.18049007
## pubt_Y1        0.48920961 0.37453324
## pubt_Y2        1.00000000 0.53597078
## pubt_Y3        0.53597078 1.00000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Create a ggheatmap for age regressed variables
ggheatmap <- ggplot(melt(cor_matrix_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Correlation matrix with covariates
# Select the variables for age regressed and covariates
allt_cov_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3", "int_p_ave", "famc_ave", "bw_lbs", "matage", "matalc_ave", "matcig_ave", "matmar_ave", "ses_lt")

# Subset the data for the selected t variables
allt_cov_data <- data_frame %>%
  select(all_of(allt_cov_variables))

# Compute the correlation matrix for age regressed vars + covariates
cor_matrix_cov_t <- cor(allt_cov_data, use = "pairwise.complete.obs")
cor_matrix_cov_t

##                intt_Baseline      intt_Y1     intt_Y2     intt_Y3
## intt_Baseline    1.000000000  0.634599505  0.55335885  0.47612108
## intt_Y1          0.634599505  1.000000000  0.61992020  0.56421070
## intt_Y2          0.553358852  0.619920198  1.00000000  0.64181976
## intt_Y3          0.476121078  0.564210695  0.64181976  1.00000000
## wchrt_Baseline   0.112748632  0.128880689  0.11523869  0.12005757
## wchrt_Y1         0.087304884  0.104518560  0.09697969  0.10571372
## wchrt_Y2         0.084856238  0.111618115  0.11984600  0.12694736
## wchrt_Y3         0.067872323  0.054964793  0.11039562  0.12093410
## pubt_Baseline    0.035283495  0.027973965  0.04656040  0.07171897
## pubt_Y1          0.031039212  0.028406239  0.06444200  0.08064207
## pubt_Y2          0.021261670  0.011269234  0.04240770  0.05764760
## pubt_Y3          0.007822800  0.010171060  0.04139724  0.07370080
## int_p_ave        0.355991007  0.367665693  0.41995073  0.35511429
## famc_ave         0.164928271  0.160871502  0.18473974  0.18633884
## bw_lbs          -0.020776935  0.020521616  0.01480217  0.04138705
## matage          -0.094918698 -0.067320296 -0.06672996 -0.06156389
## matalc_ave      -0.007530688  0.007375519  0.01133506  0.01167891
## matcig_ave       0.054665964  0.076780173  0.06140683  0.07305675
## matmar_ave       0.043304449  0.040361945  0.03272173  0.04603020
## ses_lt          -0.255607077 -0.221487877 -0.20859871 -0.21268692
##                wchrt_Baseline      wchrt_Y1      wchrt_Y2      wchrt_Y3
## intt_Baseline     0.112748632  0.0873048840  0.0848562382  0.0678723232
## intt_Y1           0.128880689  0.1045185595  0.1116181149  0.0549647932
## intt_Y2           0.115238693  0.0969796900  0.1198460047  0.1103956193
## intt_Y3           0.120057569  0.1057137227  0.1269473609  0.1209340993
## wchrt_Baseline    1.000000000  0.6476801956  0.6540028144  0.6111944327
## wchrt_Y1          0.647680196  1.0000000000  0.6640879369  0.6674085270
## wchrt_Y2          0.654002814  0.6640879369  1.0000000000  0.7665870075
## wchrt_Y3          0.611194433  0.6674085270  0.7665870075  1.0000000000
## pubt_Baseline     0.099733120  0.0958629278  0.1021776965  0.0787478853
## pubt_Y1           0.129755027  0.1290914933  0.1412016020  0.2022895353
## pubt_Y2           0.128949686  0.1050143147  0.1144494851  0.1459049692
## pubt_Y3           0.133146340  0.1061165836  0.1042413813  0.1110310300
## int_p_ave         0.074606800  0.0854224387  0.0803676945  0.0284861349
## famc_ave          0.033904905  0.0316720249  0.0328397038  0.0437816231
## bw_lbs            0.063943125  0.0615521215  0.0281735891  0.0476436872
## matage           -0.029865891 -0.0390539910 -0.0462294497 -0.0724014572
## matalc_ave        0.009328286 -0.0004684303  0.0007193362 -0.0002777456
## matcig_ave        0.130223896  0.0974661736  0.1154386013  0.2289238300
## matmar_ave        0.038651053  0.0514554115  0.0654811173  0.0628571312
## ses_lt           -0.201741488 -0.1588565450 -0.2016745704 -0.2211153951
##                pubt_Baseline     pubt_Y1      pubt_Y2     pubt_Y3     int_p_ave
## intt_Baseline    0.035283495  0.03103921  0.021261670  0.00782280  0.3559910072
## intt_Y1          0.027973965  0.02840624  0.011269234  0.01017106  0.3676656929
## intt_Y2          0.046560398  0.06444200  0.042407699  0.04139724  0.4199507286
## intt_Y3          0.071718974  0.08064207  0.057647599  0.07370080  0.3551142883
## wchrt_Baseline   0.099733120  0.12975503  0.128949686  0.13314634  0.0746068004
## wchrt_Y1         0.095862928  0.12909149  0.105014315  0.10611658  0.0854224387
## wchrt_Y2         0.102177696  0.14120160  0.114449485  0.10424138  0.0803676945
## wchrt_Y3         0.078747885  0.20228954  0.145904969  0.11103103  0.0284861349
## pubt_Baseline    1.000000000  0.36851872  0.253440563  0.18049007  0.0428625302
## pubt_Y1          0.368518723  1.00000000  0.489209605  0.37453324  0.0473883207
## pubt_Y2          0.253440563  0.48920961  1.000000000  0.53597078  0.0545221315
## pubt_Y3          0.180490066  0.37453324  0.535970775  1.00000000  0.0504080170
## int_p_ave        0.042862530  0.04738832  0.054522131  0.05040802  1.0000000000
## famc_ave         0.008702177 -0.01415702  0.001359803 -0.01843012  0.3114959034
## bw_lbs          -0.002006455  0.01304283 -0.024902989  0.01744853  0.0264148549
## matage          -0.053661373 -0.01301635 -0.019928182 -0.02183066 -0.1146062137
## matalc_ave       0.003033662  0.01960039  0.024762062  0.00640373 -0.0006641259
## matcig_ave       0.053820414  0.06709481  0.053232745  0.03238020  0.0897095246
## matmar_ave       0.028616833  0.02541711  0.016666477  0.01300408  0.0648147298
## ses_lt          -0.126051065 -0.10831892 -0.111125027 -0.10364964 -0.3661287560
##                     famc_ave       bw_lbs        matage    matalc_ave
## intt_Baseline   0.1649282710 -0.020776935 -0.0949186977 -0.0075306884
## intt_Y1         0.1608715017  0.020521616 -0.0673202957  0.0073755192
## intt_Y2         0.1847397352  0.014802170 -0.0667299564  0.0113350632
## intt_Y3         0.1863388362  0.041387053 -0.0615638851  0.0116789090
## wchrt_Baseline  0.0339049048  0.063943125 -0.0298658914  0.0093282856
## wchrt_Y1        0.0316720249  0.061552122 -0.0390539910 -0.0004684303
## wchrt_Y2        0.0328397038  0.028173589 -0.0462294497  0.0007193362
## wchrt_Y3        0.0437816231  0.047643687 -0.0724014572 -0.0002777456
## pubt_Baseline   0.0087021774 -0.002006455 -0.0536613733  0.0030336621
## pubt_Y1        -0.0141570200  0.013042831 -0.0130163526  0.0196003926
## pubt_Y2         0.0013598035 -0.024902989 -0.0199281822  0.0247620618
## pubt_Y3        -0.0184301173  0.017448529 -0.0218306597  0.0064037301
## int_p_ave       0.3114959034  0.026414855 -0.1146062137 -0.0006641259
## famc_ave        1.0000000000  0.008024666 -0.0005858859  0.0365278092
## bw_lbs          0.0080246657  1.000000000 -0.0499162070 -0.0155825153
## matage         -0.0005858859 -0.049916207  1.0000000000  0.0356733281
## matalc_ave      0.0365278092 -0.015582515  0.0356733281  1.0000000000
## matcig_ave      0.0161007397 -0.053714657 -0.1027317078  0.1998483845
## matmar_ave      0.0032220425 -0.005330046 -0.0911399455  0.0320614474
## ses_lt         -0.1300038144  0.033712893  0.4577169140 -0.0286423129
##                 matcig_ave   matmar_ave      ses_lt
## intt_Baseline   0.05466596  0.043304449 -0.25560708
## intt_Y1         0.07678017  0.040361945 -0.22148788
## intt_Y2         0.06140683  0.032721732 -0.20859871
## intt_Y3         0.07305675  0.046030201 -0.21268692
## wchrt_Baseline  0.13022390  0.038651053 -0.20174149
## wchrt_Y1        0.09746617  0.051455411 -0.15885655
## wchrt_Y2        0.11543860  0.065481117 -0.20167457
## wchrt_Y3        0.22892383  0.062857131 -0.22111540
## pubt_Baseline   0.05382041  0.028616833 -0.12605107
## pubt_Y1         0.06709481  0.025417113 -0.10831892
## pubt_Y2         0.05323275  0.016666477 -0.11112503
## pubt_Y3         0.03238020  0.013004081 -0.10364964
## int_p_ave       0.08970952  0.064814730 -0.36612876
## famc_ave        0.01610074  0.003222043 -0.13000381
## bw_lbs         -0.05371466 -0.005330046  0.03371289
## matage         -0.10273171 -0.091139946  0.45771691
## matalc_ave      0.19984838  0.032061447 -0.02864231
## matcig_ave      1.00000000  0.106555482 -0.28802399
## matmar_ave      0.10655548  1.000000000 -0.19520129
## ses_lt         -0.28802399 -0.195201287  1.00000000

# Create a ggheatmap for age regressed variables + covariates
ggheatmap <- ggplot(melt(cor_matrix_cov_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 2) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Associations (Black sample)

# subset data to just White participants
subset_all_merged <- all_merged[all_merged$race3 == 2, ]

# Examining cross phenotype associations

# Select the variables to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3",
                           "age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")

# Convert data.table to data frame
data_frame <- as.data.frame(subset_all_merged)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars    n   mean   sd median trimmed  mad    min    max range
## age_Baseline      1 1782 118.89 7.28 119.00  118.80 8.90 107.00 132.00 25.00
## int_Baseline      2 1782   1.08 1.82   0.00    0.66 0.00   0.00  12.00 12.00
## intt_Baseline     3 1781   0.06 1.81  -0.91   -0.35 0.34  -1.16  10.86 12.03
## age_Y1            4 1594 130.96 7.51 130.50  130.84 9.64 117.00 149.00 32.00
## int_Y1            5 1593   1.12 1.81   0.00    0.71 0.00   0.00  14.00 14.00
## intt_Y1           6 1592   0.01 1.81  -0.99   -0.38 0.34  -1.30  12.78 14.08
## age_Y2            7 1548 144.22 7.85 144.00  144.13 8.90 127.00 166.00 39.00
## int_Y2            8 1548   1.14 1.90   0.00    0.71 0.00   0.00  15.00 15.00
## intt_Y2           9 1547  -0.09 1.90  -1.04   -0.50 0.55  -1.64  13.66 15.30
## age_Y3           10 1327 154.78 7.65 154.00  154.67 8.90 137.00 173.00 36.00
## int_Y3           11 1327   1.26 2.07   0.00    0.78 0.00   0.00  14.00 14.00
## intt_Y3          12 1326  -0.19 2.07  -1.26   -0.64 0.59  -1.78  12.47 14.25
## age_Baseline.1   13 1782 118.89 7.28 119.00  118.80 8.90 107.00 132.00 25.00
## wchr_Baseline    14 1781   0.49 0.08   0.48    0.49 0.07   0.27   0.89  0.62
## wchrt_Baseline   15 1780   0.01 0.08   0.00    0.00 0.07  -0.21   0.41  0.62
## age_Y1.1         16 1594 130.96 7.51 130.50  130.84 9.64 117.00 149.00 32.00
## wchr_Y1          17 1567   0.50 0.08   0.48    0.49 0.08   0.30   1.00  0.70
## wchrt_Y1         18 1566   0.01 0.08   0.00    0.01 0.08  -0.18   0.52  0.70
## age_Y2.1         19 1548 144.22 7.85 144.00  144.13 8.90 127.00 166.00 39.00
## wchr_Y2          20 1192   0.50 0.10   0.48    0.49 0.08   0.30   1.41  1.10
## wchrt_Y2         21 1192   0.02 0.10   0.00    0.01 0.08  -0.18   0.92  1.10
## age_Y3.1         22 1327 154.78 7.65 154.00  154.67 8.90 137.00 173.00 36.00
## wchr_Y3          23  264   0.52 0.10   0.50    0.51 0.11   0.37   0.94  0.57
## wchrt_Y3         24  264   0.03 0.10   0.01    0.02 0.11  -0.12   0.46  0.58
## age_Baseline.2   25 1782 118.89 7.28 119.00  118.80 8.90 107.00 132.00 25.00
## pub_Baseline     26 1422   2.40 0.85   3.00    2.43 1.48   1.00   5.00  4.00
## pubt_Baseline    27 1410   0.32 0.81   0.44    0.34 0.80  -1.58   3.08  4.66
## age_Y1.2         28 1594 130.96 7.51 130.50  130.84 9.64 117.00 149.00 32.00
## pub_Y1           29  494   2.63 0.87   3.00    2.65 1.48   1.00   5.00  4.00
## pubt_Y1          30  491   0.36 0.75   0.27    0.40 0.77  -2.00   2.47  4.48
## age_Y2.2         31 1548 144.22 7.85 144.00  144.13 8.90 127.00 166.00 39.00
## pub_Y2           32 1421   2.99 0.93   3.00    3.04 1.48   1.00   5.00  4.00
## pubt_Y2          33 1420   0.28 0.75   0.37    0.31 0.71  -2.23   2.82  5.05
## age_Y3.2         34 1327 154.78 7.65 154.00  154.67 8.90 137.00 173.00 36.00
## pub_Y3           35 1239   3.32 0.88   3.00    3.38 1.48   1.00   5.00  4.00
## pubt_Y3          36 1238   0.18 0.70   0.23    0.20 0.52  -2.86   2.31  5.16
## int_p_ave        37  865   6.79 6.40   5.00    5.72 4.45   0.00  46.00 46.00
## famc_ave         38 1784   2.19 1.52   2.00    2.06 1.48   0.00   8.75  8.75
## bw_lbs           39 1554   6.65 1.44   6.69    6.68 1.30   1.81  11.56  9.75
## matage           40 1686  25.79 6.25  25.00   25.38 5.93  13.00  47.00 34.00
## matalc_ave       41 1681   0.01 0.29   0.00    0.00 0.00   0.00  10.00 10.00
## matcig_ave       42 1668   0.44 2.13   0.00    0.00 0.00   0.00  30.00 30.00
## matmar_ave       43 1667   0.07 0.41   0.00    0.00 0.00   0.00   5.00  5.00
## ses_lt           44  990  -0.92 1.02  -0.78   -0.88 1.03  -3.94   1.47  5.41
##                 skew kurtosis   se
## age_Baseline    0.06    -1.25 0.17
## int_Baseline    2.51     7.37 0.04
## intt_Baseline   2.50     7.33 0.04
## age_Y1          0.11    -1.11 0.19
## int_Y1          2.54     8.37 0.05
## intt_Y1         2.54     8.40 0.05
## age_Y2          0.11    -0.87 0.20
## int_Y2          2.69     9.87 0.05
## intt_Y2         2.66     9.67 0.05
## age_Y3          0.12    -0.97 0.21
## int_Y3          2.30     6.05 0.06
## intt_Y3         2.28     5.99 0.06
## age_Baseline.1  0.06    -1.25 0.17
## wchr_Baseline   0.82     0.65 0.00
## wchrt_Baseline  0.82     0.64 0.00
## age_Y1.1        0.11    -1.11 0.19
## wchr_Y1         0.98     1.40 0.00
## wchrt_Y1        0.98     1.40 0.00
## age_Y2.1        0.11    -0.87 0.20
## wchr_Y2         1.79     8.68 0.00
## wchrt_Y2        1.78     8.57 0.00
## age_Y3.1        0.12    -0.97 0.21
## wchr_Y3         0.85     0.55 0.01
## wchrt_Y3        0.85     0.62 0.01
## age_Baseline.2  0.06    -1.25 0.17
## pub_Baseline   -0.14    -0.38 0.02
## pubt_Baseline  -0.11    -0.15 0.02
## age_Y1.2        0.11    -1.11 0.19
## pub_Y1         -0.22    -0.36 0.04
## pubt_Y1        -0.30     0.20 0.03
## age_Y2.2        0.11    -0.87 0.20
## pub_Y2         -0.30    -0.39 0.02
## pubt_Y2        -0.37     0.53 0.02
## age_Y3.2        0.12    -0.97 0.21
## pub_Y3         -0.59     0.03 0.02
## pubt_Y3        -0.53     1.23 0.02
## int_p_ave       1.86     4.63 0.22
## famc_ave        0.86     0.69 0.04
## bw_lbs         -0.21     0.34 0.04
## matage          0.56    -0.11 0.15
## matalc_ave     27.40   865.95 0.01
## matcig_ave      7.71    80.18 0.05
## matmar_ave      7.04    53.82 0.01
## ses_lt         -0.44    -0.33 0.03

# Select the variables
all_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3","int_Baseline", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3","pubt_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Select the variables for age regressed
allt_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3")

# Subset the data for the selected variables
all_data <- data_frame %>%
  select(all_of(all_variables))

# Subset the data for the selected t variables
allt_data <- data_frame %>%
  select(all_of(allt_variables))

# Compute the correlation matrix for raw vars
cor_matrix <- cor(all_data, use = "pairwise.complete.obs")
cor_matrix

##               int_Baseline       int_Y1       int_Y2      int_Y3 wchr_Baseline
## int_Baseline   1.000000000  0.655863739  0.503440509  0.43397481   0.013110800
## int_Y1         0.655863739  1.000000000  0.609926562  0.53776520   0.015426809
## int_Y2         0.503440509  0.609926562  1.000000000  0.64902598   0.028254670
## int_Y3         0.433974812  0.537765203  0.649025984  1.00000000   0.060397820
## wchr_Baseline  0.013110800  0.015426809  0.028254670  0.06039782   1.000000000
## wchr_Y1       -0.005333566  0.017547470  0.030860816  0.06067700   0.818499248
## wchr_Y2        0.049797842  0.035695403  0.038386737  0.08946825   0.713672222
## wchr_Y3        0.186277715  0.159940247  0.081509570  0.18309904   0.743110230
## pubt_Baseline  0.018667504  0.053114251  0.061219612  0.03620911   0.067140044
## pub_Y1        -0.097590642 -0.074158097 -0.046585689 -0.02874867   0.009230123
## pub_Y2        -0.041844352  0.012311033  0.052370593  0.06294933   0.074481288
## pub_Y3        -0.029061549  0.009724576  0.002674181  0.06035082   0.072657964
##                    wchr_Y1    wchr_Y2     wchr_Y3 pubt_Baseline       pub_Y1
## int_Baseline  -0.005333566 0.04979784  0.18627772    0.01866750 -0.097590642
## int_Y1         0.017547470 0.03569540  0.15994025    0.05311425 -0.074158097
## int_Y2         0.030860816 0.03838674  0.08150957    0.06121961 -0.046585689
## int_Y3         0.060677005 0.08946825  0.18309904    0.03620911 -0.028748672
## wchr_Baseline  0.818499248 0.71367222  0.74311023    0.06714004  0.009230123
## wchr_Y1        1.000000000 0.77198961  0.79520992    0.10901911  0.017997773
## wchr_Y2        0.771989605 1.00000000  0.82481894    0.05233811  0.019995578
## wchr_Y3        0.795209922 0.82481894  1.00000000    0.10471430 -0.177094340
## pubt_Baseline  0.109019108 0.05233811  0.10471430    1.00000000  0.309587648
## pub_Y1         0.017997773 0.01999558 -0.17709434    0.30958765  1.000000000
## pub_Y2         0.051477173 0.02474927  0.04116280    0.27683917  0.554054984
## pub_Y3         0.059457581 0.07238219  0.06339584    0.21770111  0.475769365
##                    pub_Y2       pub_Y3
## int_Baseline  -0.04184435 -0.029061549
## int_Y1         0.01231103  0.009724576
## int_Y2         0.05237059  0.002674181
## int_Y3         0.06294933  0.060350820
## wchr_Baseline  0.07448129  0.072657964
## wchr_Y1        0.05147717  0.059457581
## wchr_Y2        0.02474927  0.072382192
## wchr_Y3        0.04116280  0.063395843
## pubt_Baseline  0.27683917  0.217701110
## pub_Y1         0.55405498  0.475769365
## pub_Y2         1.00000000  0.598944983
## pub_Y3         0.59894498  1.000000000

# Compute the correlation matrix for age regressed vars
cor_matrix_t <- cor(allt_data, use = "pairwise.complete.obs")
cor_matrix_t

##                intt_Baseline     intt_Y1      intt_Y2     intt_Y3
## intt_Baseline    1.000000000  0.65637574  0.507173976  0.44155003
## intt_Y1          0.656375737  1.00000000  0.610539764  0.53960614
## intt_Y2          0.507173976  0.61053976  1.000000000  0.64943743
## intt_Y3          0.441550031  0.53960614  0.649437425  1.00000000
## wchrt_Baseline   0.014943580  0.01611478  0.028326488  0.05817768
## wchrt_Y1        -0.003466749  0.01848038  0.031207540  0.05727149
## wchrt_Y2         0.050822395  0.03694035  0.036249387  0.08616715
## wchrt_Y3         0.185391809  0.15763537  0.077449060  0.17741343
## pubt_Baseline    0.022992134  0.05301337  0.057476352  0.02998917
## pubt_Y1         -0.061386057 -0.06488599 -0.019331240 -0.03641045
## pubt_Y2         -0.004360979  0.01659856  0.035883196  0.03093158
## pubt_Y3          0.024865641  0.01752589 -0.006385013  0.02921149
##                wchrt_Baseline     wchrt_Y1     wchrt_Y2    wchrt_Y3
## intt_Baseline      0.01494358 -0.003466749  0.050822395  0.18539181
## intt_Y1            0.01611478  0.018480376  0.036940347  0.15763537
## intt_Y2            0.02832649  0.031207540  0.036249387  0.07744906
## intt_Y3            0.05817768  0.057271486  0.086167146  0.17741343
## wchrt_Baseline     1.00000000  0.818791678  0.713023475  0.74704380
## wchrt_Y1           0.81879168  1.000000000  0.771999830  0.79889520
## wchrt_Y2           0.71302347  0.771999830  1.000000000  0.82481121
## wchrt_Y3           0.74704380  0.798895203  0.824811207  1.00000000
## pubt_Baseline      0.06835125  0.110798184  0.055570267  0.10815662
## pubt_Y1            0.03593826  0.029604641  0.026677779 -0.13120597
## pubt_Y2            0.07530620  0.043223259 -0.003992287  0.03376282
## pubt_Y3            0.06137307  0.035523913  0.048612998  0.07093859
##                pubt_Baseline     pubt_Y1      pubt_Y2      pubt_Y3
## intt_Baseline     0.02299213 -0.06138606 -0.004360979  0.024865641
## intt_Y1           0.05301337 -0.06488599  0.016598562  0.017525889
## intt_Y2           0.05747635 -0.01933124  0.035883196 -0.006385013
## intt_Y3           0.02998917 -0.03641045  0.030931585  0.029211487
## wchrt_Baseline    0.06835125  0.03593826  0.075306196  0.061373072
## wchrt_Y1          0.11079818  0.02960464  0.043223259  0.035523913
## wchrt_Y2          0.05557027  0.02667778 -0.003992287  0.048612998
## wchrt_Y3          0.10815662 -0.13120597  0.033762823  0.070938586
## pubt_Baseline     1.00000000  0.29517518  0.264198237  0.164796337
## pubt_Y1           0.29517518  1.00000000  0.390362509  0.243354015
## pubt_Y2           0.26419824  0.39036251  1.000000000  0.383221767
## pubt_Y3           0.16479634  0.24335401  0.383221767  1.000000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Create a ggheatmap for age regressed variables
ggheatmap <- ggplot(melt(cor_matrix_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Correlation matrix with covariates
# Select the variables for age regressed and covariates
allt_cov_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3", "int_p_ave", "famc_ave", "bw_lbs", "matage", "matalc_ave", "matcig_ave", "matmar_ave", "ses_lt")

# Subset the data for the selected t variables
allt_cov_data <- data_frame %>%
  select(all_of(allt_cov_variables))

# Compute the correlation matrix for age regressed vars + covariates
cor_matrix_cov_t <- cor(allt_cov_data, use = "pairwise.complete.obs")
cor_matrix_cov_t

##                intt_Baseline     intt_Y1      intt_Y2     intt_Y3
## intt_Baseline    1.000000000  0.65637574  0.507173976  0.44155003
## intt_Y1          0.656375737  1.00000000  0.610539764  0.53960614
## intt_Y2          0.507173976  0.61053976  1.000000000  0.64943743
## intt_Y3          0.441550031  0.53960614  0.649437425  1.00000000
## wchrt_Baseline   0.014943580  0.01611478  0.028326488  0.05817768
## wchrt_Y1        -0.003466749  0.01848038  0.031207540  0.05727149
## wchrt_Y2         0.050822395  0.03694035  0.036249387  0.08616715
## wchrt_Y3         0.185391809  0.15763537  0.077449060  0.17741343
## pubt_Baseline    0.022992134  0.05301337  0.057476352  0.02998917
## pubt_Y1         -0.061386057 -0.06488599 -0.019331240 -0.03641045
## pubt_Y2         -0.004360979  0.01659856  0.035883196  0.03093158
## pubt_Y3          0.024865641  0.01752589 -0.006385013  0.02921149
## int_p_ave        0.421212163  0.46334330  0.496096102  0.40640343
## famc_ave         0.199746396  0.19949347  0.206924710  0.24817011
## bw_lbs           0.050932027  0.04564774  0.036785459  0.02395145
## matage          -0.120387616 -0.06379329 -0.016063842 -0.01453504
## matalc_ave       0.102789525  0.08082069  0.115964165  0.10512536
## matcig_ave       0.113029407  0.14072590  0.132904346  0.14565307
## matmar_ave       0.091859538  0.05433262  0.094259714  0.07870112
## ses_lt          -0.323955930 -0.25173088 -0.189327772 -0.16325233
##                wchrt_Baseline     wchrt_Y1     wchrt_Y2    wchrt_Y3
## intt_Baseline     0.014943580 -0.003466749  0.050822395  0.18539181
## intt_Y1           0.016114779  0.018480376  0.036940347  0.15763537
## intt_Y2           0.028326488  0.031207540  0.036249387  0.07744906
## intt_Y3           0.058177676  0.057271486  0.086167146  0.17741343
## wchrt_Baseline    1.000000000  0.818791678  0.713023475  0.74704380
## wchrt_Y1          0.818791678  1.000000000  0.771999830  0.79889520
## wchrt_Y2          0.713023475  0.771999830  1.000000000  0.82481121
## wchrt_Y3          0.747043804  0.798895203  0.824811207  1.00000000
## pubt_Baseline     0.068351250  0.110798184  0.055570267  0.10815662
## pubt_Y1           0.035938261  0.029604641  0.026677779 -0.13120597
## pubt_Y2           0.075306196  0.043223259 -0.003992287  0.03376282
## pubt_Y3           0.061373072  0.035523913  0.048612998  0.07093859
## int_p_ave         0.017334901  0.046000082  0.053345119  0.21580625
## famc_ave         -0.017268735  0.008277899  0.007208506  0.04336610
## bw_lbs            0.130220471  0.110846534  0.141264039  0.17979175
## matage            0.016653165  0.021906118  0.017768144 -0.04200944
## matalc_ave        0.007459777  0.001619303 -0.011034741 -0.10758168
## matcig_ave        0.012351970  0.029485148  0.023419434  0.12011194
## matmar_ave        0.067598406  0.071049717  0.053582267 -0.03054400
## ses_lt           -0.112859480 -0.122390813 -0.160839852 -0.06626089
##                pubt_Baseline       pubt_Y1       pubt_Y2      pubt_Y3
## intt_Baseline    0.022992134 -0.0613860574 -0.0043609786  0.024865641
## intt_Y1          0.053013371 -0.0648859938  0.0165985618  0.017525889
## intt_Y2          0.057476352 -0.0193312404  0.0358831958 -0.006385013
## intt_Y3          0.029989165 -0.0364104515  0.0309315850  0.029211487
## wchrt_Baseline   0.068351250  0.0359382613  0.0753061962  0.061373072
## wchrt_Y1         0.110798184  0.0296046409  0.0432232586  0.035523913
## wchrt_Y2         0.055570267  0.0266777791 -0.0039922865  0.048612998
## wchrt_Y3         0.108156618 -0.1312059705  0.0337628234  0.070938586
## pubt_Baseline    1.000000000  0.2951751783  0.2641982370  0.164796337
## pubt_Y1          0.295175178  1.0000000000  0.3903625085  0.243354015
## pubt_Y2          0.264198237  0.3903625085  1.0000000000  0.383221767
## pubt_Y3          0.164796337  0.2433540149  0.3832217665  1.000000000
## int_p_ave        0.013085427 -0.1087880663  0.0552432734  0.022846031
## famc_ave         0.012626390 -0.0422500879 -0.0007068531 -0.038171373
## bw_lbs          -0.007809493 -0.0215455443  0.0693306304  0.001464377
## matage          -0.019306092  0.0003169423 -0.0374793519 -0.049681442
## matalc_ave      -0.010421519 -0.1053055937  0.0131094417 -0.017661627
## matcig_ave      -0.009911451 -0.0316639305  0.0004561523 -0.029974819
## matmar_ave       0.012316210  0.0207164098  0.0099918536 -0.007285697
## ses_lt          -0.046380952  0.0512215865 -0.0119463108 -0.039889144
##                  int_p_ave      famc_ave        bw_lbs        matage
## intt_Baseline   0.42121216  0.1997463958  0.0509320265 -0.1203876156
## intt_Y1         0.46334330  0.1994934739  0.0456477444 -0.0637932854
## intt_Y2         0.49609610  0.2069247105  0.0367854586 -0.0160638420
## intt_Y3         0.40640343  0.2481701085  0.0239514507 -0.0145350419
## wchrt_Baseline  0.01733490 -0.0172687346  0.1302204708  0.0166531646
## wchrt_Y1        0.04600008  0.0082778990  0.1108465338  0.0219061176
## wchrt_Y2        0.05334512  0.0072085059  0.1412640394  0.0177681439
## wchrt_Y3        0.21580625  0.0433661017  0.1797917493 -0.0420094371
## pubt_Baseline   0.01308543  0.0126263899 -0.0078094929 -0.0193060916
## pubt_Y1        -0.10878807 -0.0422500879 -0.0215455443  0.0003169423
## pubt_Y2         0.05524327 -0.0007068531  0.0693306304 -0.0374793519
## pubt_Y3         0.02284603 -0.0381713734  0.0014643773 -0.0496814424
## int_p_ave       1.00000000  0.3607690458  0.0370662595 -0.0140296947
## famc_ave        0.36076905  1.0000000000 -0.0075530403 -0.0809355918
## bw_lbs          0.03706626 -0.0075530403  1.0000000000  0.0147111410
## matage         -0.01402969 -0.0809355918  0.0147111410  1.0000000000
## matalc_ave      0.04509212  0.0780947848 -0.0025326558  0.0073298354
## matcig_ave      0.12420204  0.0511935851 -0.0550941285  0.0032175312
## matmar_ave      0.15029203  0.0274925481 -0.0001781025 -0.0394385635
## ses_lt         -0.32319718 -0.2797967225  0.0107788491  0.3304060521
##                  matalc_ave    matcig_ave    matmar_ave      ses_lt
## intt_Baseline   0.102789525  0.1130294065  0.0918595383 -0.32395593
## intt_Y1         0.080820690  0.1407258972  0.0543326243 -0.25173088
## intt_Y2         0.115964165  0.1329043457  0.0942597137 -0.18932777
## intt_Y3         0.105125359  0.1456530689  0.0787011242 -0.16325233
## wchrt_Baseline  0.007459777  0.0123519696  0.0675984059 -0.11285948
## wchrt_Y1        0.001619303  0.0294851477  0.0710497170 -0.12239081
## wchrt_Y2       -0.011034741  0.0234194336  0.0535822670 -0.16083985
## wchrt_Y3       -0.107581678  0.1201119413 -0.0305439977 -0.06626089
## pubt_Baseline  -0.010421519 -0.0099114513  0.0123162097 -0.04638095
## pubt_Y1        -0.105305594 -0.0316639305  0.0207164098  0.05122159
## pubt_Y2         0.013109442  0.0004561523  0.0099918536 -0.01194631
## pubt_Y3        -0.017661627 -0.0299748194 -0.0072856969 -0.03988914
## int_p_ave       0.045092120  0.1242020404  0.1502920286 -0.32319718
## famc_ave        0.078094785  0.0511935851  0.0274925481 -0.27979672
## bw_lbs         -0.002532656 -0.0550941285 -0.0001781025  0.01077885
## matage          0.007329835  0.0032175312 -0.0394385635  0.33040605
## matalc_ave      1.000000000  0.0553204295  0.0652208584 -0.03140042
## matcig_ave      0.055320430  1.0000000000  0.1954797911 -0.16341217
## matmar_ave      0.065220858  0.1954797911  1.0000000000 -0.10344565
## ses_lt         -0.031400424 -0.1634121681 -0.1034456492  1.00000000

# Create a ggheatmap for age regressed variables + covariates
ggheatmap <- ggplot(melt(cor_matrix_cov_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 2) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Associations (Hispanic sample)

# subset data to just White participants
subset_all_merged <- all_merged[all_merged$race3 == 3, ]

# Examining cross phenotype associations

# Select the variables to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3",
                           "age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")

# Convert data.table to data frame
data_frame <- as.data.frame(subset_all_merged)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars    n   mean   sd median trimmed   mad    min    max range
## age_Baseline      1 2408 118.54 7.55 118.00  118.37 10.38 107.00 133.00 26.00
## int_Baseline      2 2408   1.15 1.83   0.00    0.73  0.00   0.00  15.00 15.00
## intt_Baseline     3 2407   0.12 1.83  -0.91   -0.28  0.36  -1.16  13.91 15.08
## age_Y1            4 2215 130.48 7.74 130.00  130.34 10.38 117.00 147.00 30.00
## int_Y1            5 2215   1.22 1.88   0.00    0.80  0.00   0.00  13.00 13.00
## intt_Y1           6 2214   0.12 1.88  -0.97   -0.29  0.40  -1.28  11.91 13.19
## age_Y2            7 2144 143.76 8.07 144.00  143.63 10.38 128.00 165.00 37.00
## int_Y2            8 2144   1.36 2.12   0.00    0.88  0.00   0.00  16.00 16.00
## intt_Y2           9 2143   0.14 2.12  -0.99   -0.32  0.71  -1.62  15.03 16.65
## age_Y3           10 2011 154.40 7.84 154.00  154.27 10.38 138.00 173.00 35.00
## int_Y3           11 2010   1.53 2.22   1.00    1.05  1.48   0.00  15.00 15.00
## intt_Y3          12 2009   0.09 2.21  -0.56   -0.36  1.33  -1.78  13.57 15.36
## age_Baseline.1   13 2408 118.54 7.55 118.00  118.37 10.38 107.00 133.00 26.00
## wchr_Baseline    14 2403   0.51 0.08   0.50    0.50  0.07   0.24   1.37  1.13
## wchrt_Baseline   15 2402   0.03 0.08   0.02    0.02  0.07  -0.24   0.89  1.13
## age_Y1.1         16 2215 130.48 7.74 130.00  130.34 10.38 117.00 147.00 30.00
## wchr_Y1          17 2205   0.51 0.08   0.49    0.50  0.08   0.29   1.47  1.19
## wchrt_Y1         18 2204   0.03 0.08   0.01    0.02  0.08  -0.20   1.00  1.19
## age_Y2.1         19 2144 143.76 8.07 144.00  143.63 10.38 128.00 165.00 37.00
## wchr_Y2          20 1709   0.51 0.08   0.49    0.50  0.08   0.34   0.89  0.55
## wchrt_Y2         21 1708   0.02 0.08   0.01    0.02  0.08  -0.15   0.41  0.56
## age_Y3.1         22 2011 154.40 7.84 154.00  154.27 10.38 138.00 173.00 35.00
## wchr_Y3          23  377   0.52 0.10   0.50    0.51  0.09   0.36   1.19  0.83
## wchrt_Y3         24  376   0.03 0.10   0.01    0.02  0.09  -0.13   0.71  0.83
## age_Baseline.2   25 2408 118.54 7.55 118.00  118.37 10.38 107.00 133.00 26.00
## pub_Baseline     26 1868   2.12 0.86   2.00    2.11  1.48   1.00   5.00  4.00
## pubt_Baseline    27 1857   0.05 0.83   0.05    0.05  1.18  -1.58   3.08  4.66
## age_Y1.2         28 2215 130.48 7.74 130.00  130.34 10.38 117.00 147.00 30.00
## pub_Y1           29  853   2.38 0.92   2.00    2.34  1.48   1.00   5.00  4.00
## pubt_Y1          30  845   0.12 0.82   0.11    0.14  1.07  -2.00   2.83  4.83
## age_Y2.2         31 2144 143.76 8.07 144.00  143.63 10.38 128.00 165.00 37.00
## pub_Y2           32 2018   2.83 0.97   3.00    2.91  1.48   1.00   5.00  4.00
## pubt_Y2          33 2017   0.16 0.79   0.23    0.20  0.75  -2.69   3.02  5.70
## age_Y3.2         34 2011 154.40 7.84 154.00  154.27 10.38 138.00 173.00 35.00
## pub_Y3           35 1946   3.24 0.91   3.00    3.34  1.48   1.00   5.00  4.00
## pubt_Y3          36 1945   0.13 0.74   0.22    0.17  0.57  -2.80   2.53  5.34
## int_p_ave        37 1709   7.73 6.41   6.00    6.78  5.19   0.00  44.00 44.00
## famc_ave         38 2410   2.04 1.44   1.75    1.88  1.48   0.00   7.75  7.75
## bw_lbs           39 2041   7.12 1.46   7.25    7.18  1.20   2.31  14.75 12.44
## matage           40 2348  28.05 6.53  28.00   27.89  7.41  14.00  60.00 46.00
## matalc_ave       41 2358   0.09 1.70   0.00    0.00  0.00   0.00  60.00 60.00
## matcig_ave       42 2357   0.16 1.22   0.00    0.00  0.00   0.00  20.00 20.00
## matmar_ave       43 2355   0.02 0.24   0.00    0.00  0.00   0.00   8.00  8.00
## ses_lt           44 1516  -0.28 0.87  -0.16   -0.20  0.82  -3.55   1.69  5.24
##                 skew kurtosis   se
## age_Baseline    0.13    -1.29 0.15
## int_Baseline    2.41     7.27 0.04
## intt_Baseline   2.41     7.32 0.04
## age_Y1          0.11    -1.20 0.16
## int_Y1          2.24     5.82 0.04
## intt_Y1         2.24     5.84 0.04
## age_Y2          0.14    -0.93 0.17
## int_Y2          2.21     5.76 0.05
## intt_Y2         2.20     5.75 0.05
## age_Y3          0.12    -1.02 0.17
## int_Y3          2.11     5.38 0.05
## intt_Y3         2.09     5.32 0.05
## age_Baseline.1  0.13    -1.29 0.15
## wchr_Baseline   1.54     9.15 0.00
## wchrt_Baseline  1.53     9.12 0.00
## age_Y1.1        0.11    -1.20 0.16
## wchr_Y1         1.67    10.83 0.00
## wchrt_Y1        1.69    10.99 0.00
## age_Y2.1        0.14    -0.93 0.17
## wchr_Y2         0.82     0.73 0.00
## wchrt_Y2        0.82     0.72 0.00
## age_Y3.1        0.12    -1.02 0.17
## wchr_Y3         1.49     6.08 0.00
## wchrt_Y3        1.49     6.17 0.00
## age_Baseline.2  0.13    -1.29 0.15
## pub_Baseline    0.19    -0.67 0.02
## pubt_Baseline   0.14    -0.54 0.02
## age_Y1.2        0.11    -1.20 0.16
## pub_Y1          0.09    -0.61 0.03
## pubt_Y1        -0.10    -0.47 0.03
## age_Y2.2        0.14    -0.93 0.17
## pub_Y2         -0.33    -0.74 0.02
## pubt_Y2        -0.41     0.27 0.02
## age_Y3.2        0.12    -1.02 0.17
## pub_Y3         -0.74     0.06 0.02
## pubt_Y3        -0.67     1.28 0.02
## int_p_ave       1.51     2.82 0.16
## famc_ave        0.97     0.77 0.03
## bw_lbs         -0.26     1.27 0.03
## matage          0.24    -0.44 0.13
## matalc_ave     30.13   977.83 0.03
## matcig_ave     10.15   122.82 0.03
## matmar_ave     22.05   617.96 0.00
## ses_lt         -0.85     0.78 0.02

# Select the variables
all_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3","int_Baseline", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3","pubt_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Select the variables for age regressed
allt_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3")

# Subset the data for the selected variables
all_data <- data_frame %>%
  select(all_of(all_variables))

# Subset the data for the selected t variables
allt_data <- data_frame %>%
  select(all_of(allt_variables))

# Compute the correlation matrix for raw vars
cor_matrix <- cor(all_data, use = "pairwise.complete.obs")
cor_matrix

##               int_Baseline     int_Y1     int_Y2     int_Y3 wchr_Baseline
## int_Baseline   1.000000000 0.60270184 0.53573295 0.45969906    0.09454427
## int_Y1         0.602701839 1.00000000 0.61055859 0.52220674    0.12586763
## int_Y2         0.535732952 0.61055859 1.00000000 0.59985887    0.06617289
## int_Y3         0.459699062 0.52220674 0.59985887 1.00000000    0.05164465
## wchr_Baseline  0.094544274 0.12586763 0.06617289 0.05164465    1.00000000
## wchr_Y1        0.099934435 0.11913154 0.06413020 0.05049886    0.69846646
## wchr_Y2        0.115930357 0.12025362 0.09455314 0.06966075    0.70542276
## wchr_Y3        0.143438323 0.13914024 0.12771713 0.08898117    0.60822109
## pubt_Baseline  0.060521398 0.04969004 0.04601167 0.04895839    0.05675837
## pub_Y1         0.037607918 0.03431242 0.05961206 0.12920160    0.01090057
## pub_Y2        -0.004755301 0.03114834 0.06488880 0.10469344    0.04700926
## pub_Y3        -0.015533902 0.00916158 0.04618651 0.09871629    0.02207483
##                  wchr_Y1      wchr_Y2     wchr_Y3 pubt_Baseline      pub_Y1
## int_Baseline  0.09993444  0.115930357 0.143438323    0.06052140 0.037607918
## int_Y1        0.11913154  0.120253621 0.139140242    0.04969004 0.034312415
## int_Y2        0.06413020  0.094553143 0.127717127    0.04601167 0.059612061
## int_Y3        0.05049886  0.069660749 0.088981175    0.04895839 0.129201597
## wchr_Baseline 0.69846646  0.705422762 0.608221092    0.05675837 0.010900572
## wchr_Y1       1.00000000  0.723965704 0.668435879    0.08157854 0.026174999
## wchr_Y2       0.72396570  1.000000000 0.759213903    0.03268638 0.016207111
## wchr_Y3       0.66843588  0.759213903 1.000000000    0.10556143 0.005042967
## pubt_Baseline 0.08157854  0.032686383 0.105561431    1.00000000 0.353156151
## pub_Y1        0.02617500  0.016207111 0.005042967    0.35315615 1.000000000
## pub_Y2        0.03183742  0.007751155 0.023242962    0.16249673 0.598526450
## pub_Y3        0.01669336 -0.014237700 0.036714716    0.11999840 0.476614501
##                     pub_Y2      pub_Y3
## int_Baseline  -0.004755301 -0.01553390
## int_Y1         0.031148338  0.00916158
## int_Y2         0.064888799  0.04618651
## int_Y3         0.104693437  0.09871629
## wchr_Baseline  0.047009263  0.02207483
## wchr_Y1        0.031837423  0.01669336
## wchr_Y2        0.007751155 -0.01423770
## wchr_Y3        0.023242962  0.03671472
## pubt_Baseline  0.162496725  0.11999840
## pub_Y1         0.598526450  0.47661450
## pub_Y2         1.000000000  0.66285692
## pub_Y3         0.662856922  1.00000000

# Compute the correlation matrix for age regressed vars
cor_matrix_t <- cor(allt_data, use = "pairwise.complete.obs")
cor_matrix_t

##                intt_Baseline     intt_Y1    intt_Y2    intt_Y3 wchrt_Baseline
## intt_Baseline     1.00000000 0.603720391 0.53768290 0.46415259    0.092323723
## intt_Y1           0.60372039 1.000000000 0.61140292 0.52273514    0.125363372
## intt_Y2           0.53768290 0.611402921 1.00000000 0.60102226    0.065148034
## intt_Y3           0.46415259 0.522735145 0.60102226 1.00000000    0.053290041
## wchrt_Baseline    0.09232372 0.125363372 0.06514803 0.05329004    1.000000000
## wchrt_Y1          0.09805673 0.117990878 0.06252368 0.05176862    0.698481618
## wchrt_Y2          0.11318929 0.120366887 0.09493121 0.07125195    0.705873964
## wchrt_Y3          0.13985359 0.135677900 0.12610888 0.08721631    0.607958244
## pubt_Baseline     0.06139324 0.050491447 0.04687600 0.04931916    0.056569346
## pubt_Y1           0.04623119 0.035995541 0.06446826 0.10873906    0.005945939
## pubt_Y2           0.01779463 0.026820446 0.05920282 0.07923883    0.082531990
## pubt_Y3           0.02000534 0.007965359 0.04697729 0.07382540    0.050518150
##                  wchrt_Y1    wchrt_Y2     wchrt_Y3 pubt_Baseline      pubt_Y1
## intt_Baseline  0.09805673 0.113189289  0.139853593    0.06139324  0.046231189
## intt_Y1        0.11799088 0.120366887  0.135677900    0.05049145  0.035995541
## intt_Y2        0.06252368 0.094931211  0.126108882    0.04687600  0.064468265
## intt_Y3        0.05176862 0.071251952  0.087216312    0.04931916  0.108739064
## wchrt_Baseline 0.69848162 0.705873964  0.607958244    0.05656935  0.005945939
## wchrt_Y1       1.00000000 0.723671336  0.668069856    0.08182391  0.029249838
## wchrt_Y2       0.72367134 1.000000000  0.753390907    0.03225415  0.018635579
## wchrt_Y3       0.66806986 0.753390907  1.000000000    0.10863128 -0.007676958
## pubt_Baseline  0.08182391 0.032254154  0.108631280    1.00000000  0.380396584
## pubt_Y1        0.02924984 0.018635579 -0.007676958    0.38039658  1.000000000
## pubt_Y2        0.06642228 0.029472318  0.047922812    0.18874959  0.475962894
## pubt_Y3        0.04206637 0.004175147  0.069888631    0.13212961  0.298293974
##                   pubt_Y2     pubt_Y3
## intt_Baseline  0.01779463 0.020005343
## intt_Y1        0.02682045 0.007965359
## intt_Y2        0.05920282 0.046977286
## intt_Y3        0.07923883 0.073825398
## wchrt_Baseline 0.08253199 0.050518150
## wchrt_Y1       0.06642228 0.042066366
## wchrt_Y2       0.02947232 0.004175147
## wchrt_Y3       0.04792281 0.069888631
## pubt_Baseline  0.18874959 0.132129608
## pubt_Y1        0.47596289 0.298293974
## pubt_Y2        1.00000000 0.486616517
## pubt_Y3        0.48661652 1.000000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Create a ggheatmap for age regressed variables
ggheatmap <- ggplot(melt(cor_matrix_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Correlation matrix with covariates
# Select the variables for age regressed and covariates
allt_cov_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3", "int_p_ave", "famc_ave", "bw_lbs", "matage", "matalc_ave", "matcig_ave", "matmar_ave", "ses_lt")

# Subset the data for the selected t variables
allt_cov_data <- data_frame %>%
  select(all_of(allt_cov_variables))

# Compute the correlation matrix for age regressed vars + covariates
cor_matrix_cov_t <- cor(allt_cov_data, use = "pairwise.complete.obs")
cor_matrix_cov_t

##                intt_Baseline      intt_Y1     intt_Y2      intt_Y3
## intt_Baseline     1.00000000  0.603720391  0.53768290  0.464152588
## intt_Y1           0.60372039  1.000000000  0.61140292  0.522735145
## intt_Y2           0.53768290  0.611402921  1.00000000  0.601022258
## intt_Y3           0.46415259  0.522735145  0.60102226  1.000000000
## wchrt_Baseline    0.09232372  0.125363372  0.06514803  0.053290041
## wchrt_Y1          0.09805673  0.117990878  0.06252368  0.051768620
## wchrt_Y2          0.11318929  0.120366887  0.09493121  0.071251952
## wchrt_Y3          0.13985359  0.135677900  0.12610888  0.087216312
## pubt_Baseline     0.06139324  0.050491447  0.04687600  0.049319159
## pubt_Y1           0.04623119  0.035995541  0.06446826  0.108739064
## pubt_Y2           0.01779463  0.026820446  0.05920282  0.079238827
## pubt_Y3           0.02000534  0.007965359  0.04697729  0.073825398
## int_p_ave         0.39802507  0.358965237  0.41077528  0.371097061
## famc_ave          0.15641981  0.163385528  0.19324598  0.209520102
## bw_lbs            0.03091150  0.003882456  0.01241335  0.034920092
## matage           -0.05820601 -0.042519441 -0.01300179 -0.005191954
## matalc_ave        0.05829631 -0.005235779  0.04812132  0.041237859
## matcig_ave        0.05176057  0.041966486  0.05597373  0.016352509
## matmar_ave        0.01046488  0.026685492  0.06230283  0.050609554
## ses_lt           -0.23172843 -0.219789909 -0.19164979 -0.127749362
##                wchrt_Baseline     wchrt_Y1     wchrt_Y2     wchrt_Y3
## intt_Baseline     0.092323723  0.098056734  0.113189289  0.139853593
## intt_Y1           0.125363372  0.117990878  0.120366887  0.135677900
## intt_Y2           0.065148034  0.062523675  0.094931211  0.126108882
## intt_Y3           0.053290041  0.051768620  0.071251952  0.087216312
## wchrt_Baseline    1.000000000  0.698481618  0.705873964  0.607958244
## wchrt_Y1          0.698481618  1.000000000  0.723671336  0.668069856
## wchrt_Y2          0.705873964  0.723671336  1.000000000  0.753390907
## wchrt_Y3          0.607958244  0.668069856  0.753390907  1.000000000
## pubt_Baseline     0.056569346  0.081823905  0.032254154  0.108631280
## pubt_Y1           0.005945939  0.029249838  0.018635579 -0.007676958
## pubt_Y2           0.082531990  0.066422277  0.029472318  0.047922812
## pubt_Y3           0.050518150  0.042066366  0.004175147  0.069888631
## int_p_ave        -0.001131163  0.021013622  0.010626439  0.049046181
## famc_ave         -0.013168505 -0.020786542 -0.004645044  0.003833479
## bw_lbs            0.103886218  0.093191320  0.067325013  0.134118184
## matage           -0.019130041 -0.058032497 -0.067553489 -0.111749381
## matalc_ave        0.005262163  0.001560344  0.010001695  0.017350556
## matcig_ave        0.011188076  0.014562535  0.022865979  0.027520079
## matmar_ave       -0.016476663 -0.008182653 -0.021216292 -0.023136886
## ses_lt           -0.166460886 -0.203522314 -0.228930643 -0.280561970
##                pubt_Baseline      pubt_Y1     pubt_Y2      pubt_Y3    int_p_ave
## intt_Baseline     0.06139324  0.046231189  0.01779463  0.020005343  0.398025070
## intt_Y1           0.05049145  0.035995541  0.02682045  0.007965359  0.358965237
## intt_Y2           0.04687600  0.064468265  0.05920282  0.046977286  0.410775280
## intt_Y3           0.04931916  0.108739064  0.07923883  0.073825398  0.371097061
## wchrt_Baseline    0.05656935  0.005945939  0.08253199  0.050518150 -0.001131163
## wchrt_Y1          0.08182391  0.029249838  0.06642228  0.042066366  0.021013622
## wchrt_Y2          0.03225415  0.018635579  0.02947232  0.004175147  0.010626439
## wchrt_Y3          0.10863128 -0.007676958  0.04792281  0.069888631  0.049046181
## pubt_Baseline     1.00000000  0.380396584  0.18874959  0.132129608  0.054358132
## pubt_Y1           0.38039658  1.000000000  0.47596289  0.298293974  0.057456511
## pubt_Y2           0.18874959  0.475962894  1.00000000  0.486616517  0.023157794
## pubt_Y3           0.13212961  0.298293974  0.48661652  1.000000000  0.015359679
## int_p_ave         0.05435813  0.057456511  0.02315779  0.015359679  1.000000000
## famc_ave         -0.02931147  0.006127340 -0.02205536 -0.023596372  0.345549516
## bw_lbs            0.01664035  0.065298714 -0.02989370  0.005317744 -0.015245219
## matage           -0.06517651 -0.032213583 -0.05022099 -0.063829021  0.039997818
## matalc_ave       -0.01364370  0.049010256  0.01744267 -0.004821990  0.102346312
## matcig_ave       -0.02721274  0.041490279 -0.01906328 -0.021173379  0.117468264
## matmar_ave       -0.01021247  0.086462859  0.01336075 -0.012205886  0.024485176
## ses_lt           -0.08718362 -0.229177033 -0.09178337 -0.087562200 -0.293825883
##                    famc_ave       bw_lbs       matage   matalc_ave  matcig_ave
## intt_Baseline   0.156419806  0.030911498 -0.058206009  0.058296307  0.05176057
## intt_Y1         0.163385528  0.003882456 -0.042519441 -0.005235779  0.04196649
## intt_Y2         0.193245975  0.012413348 -0.013001792  0.048121324  0.05597373
## intt_Y3         0.209520102  0.034920092 -0.005191954  0.041237859  0.01635251
## wchrt_Baseline -0.013168505  0.103886218 -0.019130041  0.005262163  0.01118808
## wchrt_Y1       -0.020786542  0.093191320 -0.058032497  0.001560344  0.01456253
## wchrt_Y2       -0.004645044  0.067325013 -0.067553489  0.010001695  0.02286598
## wchrt_Y3        0.003833479  0.134118184 -0.111749381  0.017350556  0.02752008
## pubt_Baseline  -0.029311469  0.016640351 -0.065176508 -0.013643697 -0.02721274
## pubt_Y1         0.006127340  0.065298714 -0.032213583  0.049010256  0.04149028
## pubt_Y2        -0.022055356 -0.029893698 -0.050220988  0.017442668 -0.01906328
## pubt_Y3        -0.023596372  0.005317744 -0.063829021 -0.004821990 -0.02117338
## int_p_ave       0.345549516 -0.015245219  0.039997818  0.102346312  0.11746826
## famc_ave        1.000000000  0.008368085  0.071715358  0.034574058  0.02902606
## bw_lbs          0.008368085  1.000000000 -0.039544397 -0.016125638 -0.01186736
## matage          0.071715358 -0.039544397  1.000000000  0.025645751 -0.02100861
## matalc_ave      0.034574058 -0.016125638  0.025645751  1.000000000  0.31481809
## matcig_ave      0.029026057 -0.011867359 -0.021008608  0.314818091  1.00000000
## matmar_ave      0.045960005  0.024582786 -0.043360747  0.028942061  0.01389411
## ses_lt         -0.105304875 -0.041207534  0.432337811 -0.041312985 -0.15423670
##                  matmar_ave      ses_lt
## intt_Baseline   0.010464876 -0.23172843
## intt_Y1         0.026685492 -0.21978991
## intt_Y2         0.062302830 -0.19164979
## intt_Y3         0.050609554 -0.12774936
## wchrt_Baseline -0.016476663 -0.16646089
## wchrt_Y1       -0.008182653 -0.20352231
## wchrt_Y2       -0.021216292 -0.22893064
## wchrt_Y3       -0.023136886 -0.28056197
## pubt_Baseline  -0.010212470 -0.08718362
## pubt_Y1         0.086462859 -0.22917703
## pubt_Y2         0.013360747 -0.09178337
## pubt_Y3        -0.012205886 -0.08756220
## int_p_ave       0.024485176 -0.29382588
## famc_ave        0.045960005 -0.10530488
## bw_lbs          0.024582786 -0.04120753
## matage         -0.043360747  0.43233781
## matalc_ave      0.028942061 -0.04131299
## matcig_ave      0.013894111 -0.15423670
## matmar_ave      1.000000000 -0.06786295
## ses_lt         -0.067862948  1.00000000

# Create a ggheatmap for age regressed variables + covariates
ggheatmap <- ggplot(melt(cor_matrix_cov_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 2) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Associations (Boys)

# subset data to just White participants
subset_all_merged <- all_merged[all_merged$sex == 1, ]

# Examining cross phenotype associations

# Select the variables to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3",
                           "age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")

# Convert data.table to data frame
data_frame <- as.data.frame(subset_all_merged)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars    n   mean   sd median trimmed   mad    min    max range
## age_Baseline      1 5415 119.13 7.50 119.00  119.04 10.38 107.00 133.00 26.00
## int_Baseline      2 5415   1.11 1.78   0.00    0.72  0.00   0.00  15.00 15.00
## intt_Baseline     3 5415   0.00 1.78  -1.07   -0.39  0.12  -1.16  13.91 15.08
## age_Y1            4 5130 131.23 7.70 131.00  131.16 10.38 117.00 149.00 32.00
## int_Y1            5 5129   1.15 1.82   0.00    0.74  0.00   0.00  14.00 14.00
## intt_Y1           6 5129   0.00 1.82  -1.05   -0.40  0.29  -1.30  12.78 14.08
## age_Y2            7 5013 144.41 7.96 144.00  144.35 10.38 127.00 166.00 39.00
## int_Y2            8 5013   1.23 1.95   0.00    0.79  0.00   0.00  15.00 15.00
## intt_Y2           9 5013   0.00 1.95  -1.05   -0.42  0.52  -1.55  13.87 15.41
## age_Y3           10 4665 155.12 7.75 155.00  155.03  8.90 137.00 174.00 37.00
## int_Y3           11 4662   1.35 2.00   1.00    0.92  1.48   0.00  15.00 15.00
## intt_Y3          12 4662   0.00 2.00  -0.50   -0.42  1.30  -1.56  13.69 15.25
## age_Baseline.1   13 5415 119.13 7.50 119.00  119.04 10.38 107.00 133.00 26.00
## wchr_Baseline    14 5409   0.48 0.07   0.47    0.47  0.06   0.30   1.15  0.85
## wchrt_Baseline   15 5409   0.00 0.07  -0.01   -0.01  0.06  -0.18   0.66  0.85
## age_Y1.1         16 5130 131.23 7.70 131.00  131.16 10.38 117.00 149.00 32.00
## wchr_Y1          17 5092   0.48 0.07   0.47    0.47  0.06   0.29   1.38  1.10
## wchrt_Y1         18 5092   0.00 0.07  -0.02   -0.01  0.06  -0.20   0.90  1.10
## age_Y2.1         19 5013 144.41 7.96 144.00  144.35 10.38 127.00 166.00 39.00
## wchr_Y2          20 4203   0.48 0.08   0.46    0.47  0.06   0.31   1.41  1.10
## wchrt_Y2         21 4203   0.00 0.08  -0.02   -0.01  0.06  -0.18   0.92  1.10
## age_Y3.1         22 4665 155.12 7.75 155.00  155.03  8.90 137.00 174.00 37.00
## wchr_Y3          23  921   0.49 0.08   0.46    0.48  0.07   0.36   1.19  0.83
## wchrt_Y3         24  921   0.00 0.08  -0.02   -0.01  0.07  -0.13   0.71  0.84
## age_Baseline.2   25 5415 119.13 7.50 119.00  119.04 10.38 107.00 133.00 26.00
## pub_Baseline     26 4797   1.94 0.77   2.00    1.90  1.48   1.00   5.00  4.00
## pubt_Baseline    27 4792   0.00 0.76   0.05   -0.04  1.44  -0.97   3.08  4.05
## age_Y1.2         28 5130 131.23 7.70 131.00  131.16 10.38 117.00 149.00 32.00
## pub_Y1           29 2285   1.95 0.77   2.00    1.91  1.48   1.00   5.00  4.00
## pubt_Y1          30 2280   0.00 0.76   0.02   -0.03  1.22  -1.13   3.08  4.21
## age_Y2.2         31 5013 144.41 7.96 144.00  144.35 10.38 127.00 166.00 39.00
## pub_Y2           32 4915   2.23 0.83   2.00    2.22  1.48   1.00   5.00  4.00
## pubt_Y2          33 4915   0.00 0.79  -0.02    0.00  0.82  -1.86   3.02  4.87
## age_Y3.2         34 4665 155.12 7.75 155.00  155.03  8.90 137.00 174.00 37.00
## pub_Y3           35 4650   2.66 0.86   3.00    2.70  1.48   1.00   5.00  4.00
## pubt_Y3          36 4650   0.00 0.81   0.04    0.02  0.80  -2.15   2.53  4.68
## int_p_ave        37 4257   7.72 6.08   6.25    6.88  5.19   0.00  48.50 48.50
## famc_ave         38 5418   2.34 1.60   2.00    2.19  1.48   0.00   8.25  8.25
## bw_lbs           39 4884   7.15 1.50   7.31    7.21  1.39   2.12  14.75 12.62
## matage           40 5305  29.44 6.26  30.00   29.43  5.93  14.00  60.00 46.00
## matalc_ave       41 5279   0.06 1.17   0.00    0.00  0.00   0.00  60.00 60.00
## matcig_ave       42 5276   0.32 1.98   0.00    0.00  0.00   0.00  30.00 30.00
## matmar_ave       43 5278   0.02 0.24   0.00    0.00  0.00   0.00   8.00  8.00
## ses_lt           44 3752  -0.01 0.93   0.24    0.11  0.76  -3.94   1.59  5.53
##                 skew kurtosis   se
## age_Baseline    0.05    -1.27 0.10
## int_Baseline    2.40     7.58 0.02
## intt_Baseline   2.40     7.58 0.02
## age_Y1          0.06    -1.18 0.11
## int_Y1          2.33     6.54 0.03
## intt_Y1         2.32     6.51 0.03
## age_Y2          0.08    -0.96 0.11
## int_Y2          2.35     6.84 0.03
## intt_Y2         2.33     6.77 0.03
## age_Y3          0.08    -1.02 0.11
## int_Y3          2.04     4.82 0.03
## intt_Y3         2.03     4.77 0.03
## age_Baseline.1  0.05    -1.27 0.10
## wchr_Baseline   1.22     3.10 0.00
## wchrt_Baseline  1.22     3.09 0.00
## age_Y1.1        0.06    -1.18 0.11
## wchr_Y1         1.56     7.33 0.00
## wchrt_Y1        1.55     7.30 0.00
## age_Y2.1        0.08    -0.96 0.11
## wchr_Y2         1.81    10.53 0.00
## wchrt_Y2        1.81    10.48 0.00
## age_Y3.1        0.08    -1.02 0.11
## wchr_Y3         1.65     6.13 0.00
## wchrt_Y3        1.65     6.24 0.00
## age_Baseline.2  0.05    -1.27 0.10
## pub_Baseline    0.42    -0.19 0.01
## pubt_Baseline   0.43    -0.18 0.01
## age_Y1.2        0.06    -1.18 0.11
## pub_Y1          0.34    -0.54 0.02
## pubt_Y1         0.31    -0.57 0.02
## age_Y2.2        0.08    -0.96 0.11
## pub_Y2          0.09    -0.63 0.01
## pubt_Y2         0.07    -0.50 0.01
## age_Y3.2        0.08    -1.02 0.11
## pub_Y3         -0.23    -0.43 0.01
## pubt_Y3        -0.20    -0.27 0.01
## int_p_ave       1.45     2.83 0.09
## famc_ave        0.77     0.15 0.02
## bw_lbs         -0.28     0.35 0.02
## matage          0.03    -0.36 0.09
## matalc_ave     42.13  1979.22 0.02
## matcig_ave      8.52    86.75 0.03
## matmar_ave     17.43   379.99 0.00
## ses_lt         -1.19     1.25 0.02

# Select the variables
all_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3","int_Baseline", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3","pubt_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Select the variables for age regressed
allt_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3")

# Subset the data for the selected variables
all_data <- data_frame %>%
  select(all_of(all_variables))

# Subset the data for the selected t variables
allt_data <- data_frame %>%
  select(all_of(allt_variables))

# Compute the correlation matrix for raw vars
cor_matrix <- cor(all_data, use = "pairwise.complete.obs")
cor_matrix

##               int_Baseline      int_Y1      int_Y2     int_Y3 wchr_Baseline
## int_Baseline    1.00000000  0.63137491 0.557009005 0.50274008    0.08433382
## int_Y1          0.63137491  1.00000000 0.631225908 0.58359069    0.11097593
## int_Y2          0.55700900  0.63122591 1.000000000 0.65311341    0.07908891
## int_Y3          0.50274008  0.58359069 0.653113413 1.00000000    0.08329643
## wchr_Baseline   0.08433382  0.11097593 0.079088914 0.08329643    1.00000000
## wchr_Y1         0.08902741  0.11479823 0.095304982 0.09081946    0.74767938
## wchr_Y2         0.09652095  0.11268561 0.090420599 0.09973608    0.69810278
## wchr_Y3         0.12183640  0.10932637 0.066873910 0.08781948    0.70568090
## pubt_Baseline   0.03080922  0.01777874 0.012165741 0.03984321    0.04647517
## pub_Y1          0.01459254 -0.01900346 0.009925341 0.03400911    0.11052342
## pub_Y2          0.02494770  0.03511006 0.030144740 0.02719693    0.12450868
## pub_Y3          0.03246799  0.03344152 0.045155382 0.06054504    0.11950641
##                  wchr_Y1    wchr_Y2    wchr_Y3 pubt_Baseline       pub_Y1
## int_Baseline  0.08902741 0.09652095 0.12183640    0.03080922  0.014592542
## int_Y1        0.11479823 0.11268561 0.10932637    0.01777874 -0.019003458
## int_Y2        0.09530498 0.09042060 0.06687391    0.01216574  0.009925341
## int_Y3        0.09081946 0.09973608 0.08781948    0.03984321  0.034009114
## wchr_Baseline 0.74767938 0.69810278 0.70568090    0.04647517  0.110523420
## wchr_Y1       1.00000000 0.74419085 0.74822625    0.06466979  0.085901713
## wchr_Y2       0.74419085 1.00000000 0.80498405    0.04257451  0.064460817
## wchr_Y3       0.74822625 0.80498405 1.00000000    0.06211216  0.080434964
## pubt_Baseline 0.06466979 0.04257451 0.06211216    1.00000000  0.309839341
## pub_Y1        0.08590171 0.06446082 0.08043496    0.30983934  1.000000000
## pub_Y2        0.08543944 0.04210667 0.04729826    0.20078123  0.442810016
## pub_Y3        0.08306037 0.03883849 0.05209544    0.14792894  0.335288247
##                   pub_Y2     pub_Y3
## int_Baseline  0.02494770 0.03246799
## int_Y1        0.03511006 0.03344152
## int_Y2        0.03014474 0.04515538
## int_Y3        0.02719693 0.06054504
## wchr_Baseline 0.12450868 0.11950641
## wchr_Y1       0.08543944 0.08306037
## wchr_Y2       0.04210667 0.03883849
## wchr_Y3       0.04729826 0.05209544
## pubt_Baseline 0.20078123 0.14792894
## pub_Y1        0.44281002 0.33528825
## pub_Y2        1.00000000 0.54959889
## pub_Y3        0.54959889 1.00000000

# Compute the correlation matrix for age regressed vars
cor_matrix_t <- cor(allt_data, use = "pairwise.complete.obs")
cor_matrix_t

##                intt_Baseline     intt_Y1     intt_Y2    intt_Y3 wchrt_Baseline
## intt_Baseline     1.00000000  0.63125420 0.557213452 0.50296261     0.08451420
## intt_Y1           0.63125420  1.00000000 0.630861855 0.58330574     0.11116722
## intt_Y2           0.55721345  0.63086186 1.000000000 0.65273515     0.08009033
## intt_Y3           0.50296261  0.58330574 0.652735152 1.00000000     0.08352809
## wchrt_Baseline    0.08451420  0.11116722 0.080090327 0.08352809     1.00000000
## wchrt_Y1          0.08935389  0.11534966 0.097428562 0.09172473     0.74766747
## wchrt_Y2          0.09645357  0.11496886 0.093230534 0.10107766     0.69754146
## wchrt_Y3          0.11865054  0.10778030 0.066966183 0.08518181     0.70844093
## pubt_Baseline     0.03080895  0.01777450 0.013278505 0.04055903     0.04647451
## pubt_Y1           0.01940711 -0.02065375 0.003826305 0.03079306     0.11260606
## pubt_Y2           0.02042759  0.02392324 0.012080869 0.01746976     0.13457457
## pubt_Y3           0.02922030  0.02198955 0.026405710 0.04690541     0.12991048
##                  wchrt_Y1   wchrt_Y2   wchrt_Y3 pubt_Baseline      pubt_Y1
## intt_Baseline  0.08935389 0.09645357 0.11865054    0.03080895  0.019407106
## intt_Y1        0.11534966 0.11496886 0.10778030    0.01777450 -0.020653749
## intt_Y2        0.09742856 0.09323053 0.06696618    0.01327851  0.003826305
## intt_Y3        0.09172473 0.10107766 0.08518181    0.04055903  0.030793061
## wchrt_Baseline 0.74766747 0.69754146 0.70844093    0.04647451  0.112606062
## wchrt_Y1       1.00000000 0.74315473 0.75024380    0.06467818  0.091493882
## wchrt_Y2       0.74315473 1.00000000 0.80465842    0.04207712  0.072316154
## wchrt_Y3       0.75024380 0.80465842 1.00000000    0.06054914  0.098243650
## pubt_Baseline  0.06467818 0.04207712 0.06054914    1.00000000  0.315295526
## pubt_Y1        0.09149388 0.07231615 0.09824365    0.31529553  1.000000000
## pubt_Y2        0.09930383 0.05847450 0.06974588    0.21833934  0.428090051
## pubt_Y3        0.09607269 0.06256240 0.08146684    0.16057450  0.311742329
##                   pubt_Y2    pubt_Y3
## intt_Baseline  0.02042759 0.02922030
## intt_Y1        0.02392324 0.02198955
## intt_Y2        0.01208087 0.02640571
## intt_Y3        0.01746976 0.04690541
## wchrt_Baseline 0.13457457 0.12991048
## wchrt_Y1       0.09930383 0.09607269
## wchrt_Y2       0.05847450 0.06256240
## wchrt_Y3       0.06974588 0.08146684
## pubt_Baseline  0.21833934 0.16057450
## pubt_Y1        0.42809005 0.31174233
## pubt_Y2        1.00000000 0.49600684
## pubt_Y3        0.49600684 1.00000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Create a ggheatmap for age regressed variables
ggheatmap <- ggplot(melt(cor_matrix_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Correlation matrix with covariates
# Select the variables for age regressed and covariates
allt_cov_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3", "int_p_ave", "famc_ave", "bw_lbs", "matage", "matalc_ave", "matcig_ave", "matmar_ave", "ses_lt")

# Subset the data for the selected t variables
allt_cov_data <- data_frame %>%
  select(all_of(allt_cov_variables))

# Compute the correlation matrix for age regressed vars + covariates
cor_matrix_cov_t <- cor(allt_cov_data, use = "pairwise.complete.obs")
cor_matrix_cov_t

##                intt_Baseline      intt_Y1      intt_Y2     intt_Y3
## intt_Baseline    1.000000000  0.631254199  0.557213452  0.50296261
## intt_Y1          0.631254199  1.000000000  0.630861855  0.58330574
## intt_Y2          0.557213452  0.630861855  1.000000000  0.65273515
## intt_Y3          0.502962607  0.583305739  0.652735152  1.00000000
## wchrt_Baseline   0.084514198  0.111167220  0.080090327  0.08352809
## wchrt_Y1         0.089353887  0.115349665  0.097428562  0.09172473
## wchrt_Y2         0.096453575  0.114968864  0.093230534  0.10107766
## wchrt_Y3         0.118650538  0.107780301  0.066966183  0.08518181
## pubt_Baseline    0.030808954  0.017774500  0.013278505  0.04055903
## pubt_Y1          0.019407106 -0.020653749  0.003826305  0.03079306
## pubt_Y2          0.020427590  0.023923240  0.012080869  0.01746976
## pubt_Y3          0.029220300  0.021989548  0.026405710  0.04690541
## int_p_ave        0.380730511  0.376291987  0.415035788  0.39165549
## famc_ave         0.157363958  0.151224621  0.177818110  0.19113549
## bw_lbs           0.005894143  0.035554114  0.019942268  0.04774002
## matage          -0.091071163 -0.055436917 -0.041212711 -0.04562174
## matalc_ave       0.005876354  0.008004406  0.010572779  0.03333859
## matcig_ave       0.045336190  0.081263670  0.058955535  0.07926922
## matmar_ave       0.029880325  0.029168800  0.045904470  0.06565199
## ses_lt          -0.235159691 -0.186202068 -0.146156352 -0.13567424
##                wchrt_Baseline     wchrt_Y1     wchrt_Y2     wchrt_Y3
## intt_Baseline    0.0845141977  0.089353887  0.096453575  0.118650538
## intt_Y1          0.1111672197  0.115349665  0.114968864  0.107780301
## intt_Y2          0.0800903273  0.097428562  0.093230534  0.066966183
## intt_Y3          0.0835280942  0.091724727  0.101077664  0.085181814
## wchrt_Baseline   1.0000000000  0.747667475  0.697541460  0.708440926
## wchrt_Y1         0.7476674745  1.000000000  0.743154727  0.750243804
## wchrt_Y2         0.6975414596  0.743154727  1.000000000  0.804658420
## wchrt_Y3         0.7084409258  0.750243804  0.804658420  1.000000000
## pubt_Baseline    0.0464745103  0.064678178  0.042077122  0.060549143
## pubt_Y1          0.1126060621  0.091493882  0.072316154  0.098243650
## pubt_Y2          0.1345745729  0.099303831  0.058474497  0.069745883
## pubt_Y3          0.1299104787  0.096072685  0.062562400  0.081466839
## int_p_ave        0.0357380293  0.061920215  0.049731542  0.000578575
## famc_ave        -0.0290801406 -0.000213522  0.004451835  0.012420872
## bw_lbs           0.0720766911  0.077824082  0.040242591  0.115462055
## matage          -0.0556474551 -0.066376624 -0.052465847 -0.068276519
## matalc_ave      -0.0001409895 -0.002992378 -0.001816142 -0.025093432
## matcig_ave       0.0499428738  0.059046443  0.062030450  0.065648688
## matmar_ave       0.0249198685  0.053754828  0.030068912  0.026475711
## ses_lt          -0.2098365881 -0.204643243 -0.222508322 -0.181440131
##                pubt_Baseline      pubt_Y1      pubt_Y2      pubt_Y3
## intt_Baseline   0.0308089543  0.019407106  0.020427590  0.029220300
## intt_Y1         0.0177745000 -0.020653749  0.023923240  0.021989548
## intt_Y2         0.0132785053  0.003826305  0.012080869  0.026405710
## intt_Y3         0.0405590258  0.030793061  0.017469763  0.046905409
## wchrt_Baseline  0.0464745103  0.112606062  0.134574573  0.129910479
## wchrt_Y1        0.0646781778  0.091493882  0.099303831  0.096072685
## wchrt_Y2        0.0420771222  0.072316154  0.058474497  0.062562400
## wchrt_Y3        0.0605491432  0.098243650  0.069745883  0.081466839
## pubt_Baseline   1.0000000000  0.315295526  0.218339340  0.160574500
## pubt_Y1         0.3152955259  1.000000000  0.428090051  0.311742329
## pubt_Y2         0.2183393395  0.428090051  1.000000000  0.496006844
## pubt_Y3         0.1605745000  0.311742329  0.496006844  1.000000000
## int_p_ave       0.0115126271  0.030889228  0.044751373  0.050204735
## famc_ave        0.0049669555 -0.007158929 -0.011140275 -0.019790730
## bw_lbs         -0.0248568614 -0.004313385 -0.030521319  0.003415325
## matage         -0.0640713015 -0.063410704 -0.086962413 -0.077476546
## matalc_ave     -0.0087923468  0.024972342  0.015895671 -0.001272120
## matcig_ave     -0.0007969318  0.037376831  0.007156975 -0.003615720
## matmar_ave      0.0234927700  0.048160683  0.010250948 -0.002571770
## ses_lt         -0.1334724578 -0.185162639 -0.168097056 -0.150742501
##                   int_p_ave     famc_ave       bw_lbs      matage    matalc_ave
## intt_Baseline   0.380730511  0.157363958  0.005894143 -0.09107116  0.0058763541
## intt_Y1         0.376291987  0.151224621  0.035554114 -0.05543692  0.0080044056
## intt_Y2         0.415035788  0.177818110  0.019942268 -0.04121271  0.0105727793
## intt_Y3         0.391655488  0.191135488  0.047740023 -0.04562174  0.0333385949
## wchrt_Baseline  0.035738029 -0.029080141  0.072076691 -0.05564746 -0.0001409895
## wchrt_Y1        0.061920215 -0.000213522  0.077824082 -0.06637662 -0.0029923778
## wchrt_Y2        0.049731542  0.004451835  0.040242591 -0.05246585 -0.0018161424
## wchrt_Y3        0.000578575  0.012420872  0.115462055 -0.06827652 -0.0250934324
## pubt_Baseline   0.011512627  0.004966955 -0.024856861 -0.06407130 -0.0087923468
## pubt_Y1         0.030889228 -0.007158929 -0.004313385 -0.06341070  0.0249723420
## pubt_Y2         0.044751373 -0.011140275 -0.030521319 -0.08696241  0.0158956707
## pubt_Y3         0.050204735 -0.019790730  0.003415325 -0.07747655 -0.0012721199
## int_p_ave       1.000000000  0.316216791  0.009654146 -0.06480519  0.0311110462
## famc_ave        0.316216791  1.000000000 -0.006105543  0.03024307  0.0273598891
## bw_lbs          0.009654146 -0.006105543  1.000000000 -0.01644323 -0.0252080537
## matage         -0.064805191  0.030243072 -0.016443226  1.00000000  0.0235248570
## matalc_ave      0.031111046  0.027359889 -0.025208054  0.02352486  1.0000000000
## matcig_ave      0.090940984  0.012280219 -0.057818237 -0.06272207  0.1720746778
## matmar_ave      0.047274166  0.004164946  0.003002555 -0.06999346  0.0056198206
## ses_lt         -0.303517135 -0.112991371  0.069781405  0.48541854 -0.0230118254
##                   matcig_ave   matmar_ave      ses_lt
## intt_Baseline   0.0453361897  0.029880325 -0.23515969
## intt_Y1         0.0812636699  0.029168800 -0.18620207
## intt_Y2         0.0589555350  0.045904470 -0.14615635
## intt_Y3         0.0792692219  0.065651987 -0.13567424
## wchrt_Baseline  0.0499428738  0.024919868 -0.20983659
## wchrt_Y1        0.0590464432  0.053754828 -0.20464324
## wchrt_Y2        0.0620304500  0.030068912 -0.22250832
## wchrt_Y3        0.0656486883  0.026475711 -0.18144013
## pubt_Baseline  -0.0007969318  0.023492770 -0.13347246
## pubt_Y1         0.0373768311  0.048160683 -0.18516264
## pubt_Y2         0.0071569755  0.010250948 -0.16809706
## pubt_Y3        -0.0036157205 -0.002571770 -0.15074250
## int_p_ave       0.0909409839  0.047274166 -0.30351714
## famc_ave        0.0122802186  0.004164946 -0.11299137
## bw_lbs         -0.0578182367  0.003002555  0.06978141
## matage         -0.0627220731 -0.069993457  0.48541854
## matalc_ave      0.1720746778  0.005619821 -0.02301183
## matcig_ave      1.0000000000  0.101755827 -0.20072201
## matmar_ave      0.1017558267  1.000000000 -0.14068118
## ses_lt         -0.2007220053 -0.140681178  1.00000000

# Create a ggheatmap for age regressed variables + covariates
ggheatmap <- ggplot(melt(cor_matrix_cov_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 2) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Associations (Girls)

# subset data to just White participants
subset_all_merged <- all_merged[all_merged$sex == 2, ]

# Examining cross phenotype associations

# Select the variables to describe
variables_to_describe <- c("age_Baseline", "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "age_Baseline", "wchr_Baseline", "wchrt_Baseline",
                           "age_Y1", "wchr_Y1", "wchrt_Y1",
                           "age_Y2", "wchr_Y2", "wchrt_Y2",
                           "age_Y3", "wchr_Y3", "wchrt_Y3",
                           "age_Baseline", "pub_Baseline", "pubt_Baseline",
                           "age_Y1", "pub_Y1", "pubt_Y1",
                           "age_Y2", "pub_Y2", "pubt_Y2",
                           "age_Y3", "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")

# Convert data.table to data frame
data_frame <- as.data.frame(subset_all_merged)

# Use the describe() function to obtain descriptive statistics
variable_descriptions <- describe(data_frame[variables_to_describe])

# Print the descriptive statistics
print(variable_descriptions)

##                vars    n   mean   sd median trimmed   mad    min    max range
## age_Baseline      1 4942 118.81 7.48 119.00  118.68 10.38 107.00 132.00 25.00
## int_Baseline      2 4940   0.93 1.61   0.00    0.56  0.00   0.00  13.00 13.00
## intt_Baseline     3 4940   0.00 1.61  -0.91   -0.37  0.06  -0.96  12.06 13.02
## age_Y1            4 4651 130.91 7.74 131.00  130.80 10.38 117.00 149.00 32.00
## int_Y1            5 4651   1.06 1.72   0.00    0.68  0.00   0.00  14.00 14.00
## intt_Y1           6 4651   0.00 1.72  -0.98   -0.37  0.24  -1.19  12.91 14.10
## age_Y2            7 4507 144.12 8.07 144.00  143.98 10.38 128.00 168.00 40.00
## int_Y2            8 4506   1.24 1.98   0.00    0.79  0.00   0.00  16.00 16.00
## intt_Y2           9 4506   0.00 1.97  -1.00   -0.42  0.68  -1.70  15.03 16.73
## age_Y3           10 4158 154.71 7.78 154.00  154.59  8.90 137.00 175.00 38.00
## int_Y3           11 4157   1.54 2.30   1.00    1.04  1.48   0.00  15.00 15.00
## intt_Y3          12 4157   0.00 2.30  -0.67   -0.48  1.36  -1.82  13.57 15.40
## age_Baseline.1   13 4942 118.81 7.48 119.00  118.68 10.38 107.00 132.00 25.00
## wchr_Baseline    14 4933   0.48 0.07   0.47    0.47  0.06   0.24   1.37  1.13
## wchrt_Baseline   15 4933   0.00 0.07  -0.01   -0.01  0.06  -0.24   0.89  1.13
## age_Y1.1         16 4651 130.91 7.74 131.00  130.80 10.38 117.00 149.00 32.00
## wchr_Y1          17 4619   0.48 0.08   0.47    0.47  0.06   0.27   1.47  1.21
## wchrt_Y1         18 4619   0.00 0.08  -0.02   -0.01  0.06  -0.21   1.00  1.21
## age_Y2.1         19 4507 144.12 8.07 144.00  143.98 10.38 128.00 168.00 40.00
## wchr_Y2          20 3714   0.48 0.08   0.46    0.47  0.07   0.26   1.02  0.76
## wchrt_Y2         21 3714   0.00 0.08  -0.02   -0.01  0.07  -0.22   0.54  0.76
## age_Y3.1         22 4158 154.71 7.78 154.00  154.59  8.90 137.00 175.00 38.00
## wchr_Y3          23  833   0.49 0.09   0.47    0.48  0.07   0.34   1.26  0.92
## wchrt_Y3         24  833   0.00 0.09  -0.02   -0.01  0.07  -0.15   0.77  0.92
## age_Baseline.2   25 4942 118.81 7.48 119.00  118.68 10.38 107.00 132.00 25.00
## pub_Baseline     26 3598   2.26 0.89   2.00    2.28  1.48   1.00   5.00  4.00
## pubt_Baseline    27 3571   0.00 0.86   0.05    0.02  0.98  -1.61   2.93  4.54
## age_Y1.2         28 4651 130.91 7.74 131.00  130.80 10.38 117.00 149.00 32.00
## pub_Y1           29 1961   2.64 0.89   3.00    2.67  0.00   1.00   5.00  4.00
## pubt_Y1          30 1944   0.00 0.84   0.11    0.03  0.78  -2.12   2.83  4.95
## age_Y2.2         31 4507 144.12 8.07 144.00  143.98 10.38 128.00 168.00 40.00
## pub_Y2           32 4149   3.24 0.82   3.00    3.33  1.48   1.00   5.00  4.00
## pubt_Y2          33 4149   0.00 0.76   0.08    0.06  0.63  -2.84   2.31  5.15
## age_Y3.2         34 4158 154.71 7.78 154.00  154.59  8.90 137.00 175.00 38.00
## pub_Y3           35 3942   3.66 0.69   4.00    3.72  0.00   1.00   5.00  4.00
## pubt_Y3          36 3942   0.00 0.66   0.14    0.05  0.57  -2.94   1.66  4.60
## int_p_ave        37 3793   7.57 6.15   5.75    6.69  4.82   0.00  46.00 46.00
## famc_ave         38 4945   2.16 1.53   2.00    2.02  1.48   0.00   8.75  8.75
## bw_lbs           39 4439   6.86 1.45   7.00    6.92  1.30   1.81  13.00 11.19
## matage           40 4853  29.28 6.25  29.00   29.27  7.41  13.00  52.00 39.00
## matalc_ave       41 4814   0.05 0.89   0.00    0.00  0.00   0.00  50.00 50.00
## matcig_ave       42 4808   0.33 1.92   0.00    0.00  0.00   0.00  25.00 25.00
## matmar_ave       43 4806   0.03 0.28   0.00    0.00  0.00   0.00   7.00  7.00
## ses_lt           44 3465   0.03 0.92   0.27    0.15  0.75  -3.80   1.69  5.49
##                 skew kurtosis   se
## age_Baseline    0.09    -1.26 0.11
## int_Baseline    2.65     8.79 0.02
## intt_Baseline   2.65     8.79 0.02
## age_Y1          0.09    -1.18 0.11
## int_Y1          2.54     8.24 0.03
## intt_Y1         2.54     8.23 0.03
## age_Y2          0.14    -0.90 0.12
## int_Y2          2.41     7.40 0.03
## intt_Y2         2.39     7.37 0.03
## age_Y3          0.12    -1.02 0.12
## int_Y3          2.17     5.52 0.04
## intt_Y3         2.16     5.51 0.04
## age_Baseline.1  0.09    -1.26 0.11
## wchr_Baseline   1.39     6.54 0.00
## wchrt_Baseline  1.39     6.53 0.00
## age_Y1.1        0.09    -1.18 0.11
## wchr_Y1         2.45    18.85 0.00
## wchrt_Y1        2.46    18.85 0.00
## age_Y2.1        0.14    -0.90 0.12
## wchr_Y2         1.18     2.48 0.00
## wchrt_Y2        1.18     2.46 0.00
## age_Y3.1        0.12    -1.02 0.12
## wchr_Y3         1.79     8.32 0.00
## wchrt_Y3        1.79     8.32 0.00
## age_Baseline.2  0.09    -1.26 0.11
## pub_Baseline   -0.16    -1.01 0.01
## pubt_Baseline  -0.16    -0.97 0.01
## age_Y1.2        0.09    -1.18 0.11
## pub_Y1         -0.39    -0.38 0.02
## pubt_Y1        -0.35    -0.29 0.02
## age_Y2.2        0.14    -0.90 0.12
## pub_Y2         -0.76     0.63 0.01
## pubt_Y2        -0.73     0.94 0.01
## age_Y3.2        0.12    -1.02 0.12
## pub_Y3         -1.11     2.31 0.01
## pubt_Y3        -1.01     2.27 0.01
## int_p_ave       1.43     2.36 0.10
## famc_ave        0.83     0.44 0.02
## bw_lbs         -0.37     0.27 0.02
## matage          0.02    -0.52 0.09
## matalc_ave     42.34  2154.34 0.01
## matcig_ave      7.60    65.91 0.03
## matmar_ave     11.51   168.08 0.00
## ses_lt         -1.24     1.40 0.02

# Select the variables
all_variables <- c("int_Baseline", "int_Y1", "int_Y2", "int_Y3","int_Baseline", "wchr_Baseline", "wchr_Y1", "wchr_Y2", "wchr_Y3","pubt_Baseline", "pub_Y1", "pub_Y2", "pub_Y3")

# Select the variables for age regressed
allt_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3")

# Subset the data for the selected variables
all_data <- data_frame %>%
  select(all_of(all_variables))

# Subset the data for the selected t variables
allt_data <- data_frame %>%
  select(all_of(allt_variables))

# Compute the correlation matrix for raw vars
cor_matrix <- cor(all_data, use = "pairwise.complete.obs")
cor_matrix

##               int_Baseline     int_Y1     int_Y2     int_Y3 wchr_Baseline
## int_Baseline   1.000000000 0.63006350 0.52310491 0.43399629    0.10572124
## int_Y1         0.630063500 1.00000000 0.60147440 0.52138570    0.10913467
## int_Y2         0.523104906 0.60147440 1.00000000 0.61575279    0.09407256
## int_Y3         0.433996286 0.52138570 0.61575279 1.00000000    0.09155619
## wchr_Baseline  0.105721243 0.10913467 0.09407256 0.09155619    1.00000000
## wchr_Y1        0.073842085 0.07946399 0.05955349 0.07207802    0.68767929
## wchr_Y2        0.086120394 0.09235673 0.10309424 0.10145914    0.69955008
## wchr_Y3        0.099190212 0.08318337 0.14616349 0.14505898    0.61345435
## pubt_Baseline  0.067207131 0.07240414 0.08618011 0.07027137    0.18867303
## pub_Y1         0.029367627 0.06751000 0.10111957 0.10496780    0.11479372
## pub_Y2         0.034208870 0.03487927 0.10900282 0.09878727    0.14869608
## pub_Y3         0.004310881 0.01433558 0.07051692 0.09752480    0.12638938
##                  wchr_Y1    wchr_Y2    wchr_Y3 pubt_Baseline     pub_Y1
## int_Baseline  0.07384209 0.08612039 0.09919021    0.06720713 0.02936763
## int_Y1        0.07946399 0.09235673 0.08318337    0.07240414 0.06751000
## int_Y2        0.05955349 0.10309424 0.14616349    0.08618011 0.10111957
## int_Y3        0.07207802 0.10145914 0.14505898    0.07027137 0.10496780
## wchr_Baseline 0.68767929 0.69955008 0.61345435    0.18867303 0.11479372
## wchr_Y1       1.00000000 0.69273414 0.68083349    0.18532971 0.13210842
## wchr_Y2       0.69273414 1.00000000 0.77097119    0.19604803 0.18818961
## wchr_Y3       0.68083349 0.77097119 1.00000000    0.19080757 0.18174839
## pubt_Baseline 0.18532971 0.19604803 0.19080757    1.00000000 0.43338964
## pub_Y1        0.13210842 0.18818961 0.18174839    0.43338964 1.00000000
## pub_Y2        0.12712810 0.18295262 0.23946693    0.31900504 0.62422135
## pub_Y3        0.11684900 0.15264140 0.18617456    0.23393737 0.50676969
##                   pub_Y2      pub_Y3
## int_Baseline  0.03420887 0.004310881
## int_Y1        0.03487927 0.014335584
## int_Y2        0.10900282 0.070516920
## int_Y3        0.09878727 0.097524801
## wchr_Baseline 0.14869608 0.126389376
## wchr_Y1       0.12712810 0.116848997
## wchr_Y2       0.18295262 0.152641402
## wchr_Y3       0.23946693 0.186174560
## pubt_Baseline 0.31900504 0.233937366
## pub_Y1        0.62422135 0.506769687
## pub_Y2        1.00000000 0.608902237
## pub_Y3        0.60890224 1.000000000

# Compute the correlation matrix for age regressed vars
cor_matrix_t <- cor(allt_data, use = "pairwise.complete.obs")
cor_matrix_t

##                intt_Baseline     intt_Y1    intt_Y2    intt_Y3 wchrt_Baseline
## intt_Baseline    1.000000000 0.630156041 0.52360544 0.43398938     0.10594075
## intt_Y1          0.630156041 1.000000000 0.60072899 0.52103491     0.10965719
## intt_Y2          0.523605440 0.600728992 1.00000000 0.61551840     0.09526343
## intt_Y3          0.433989378 0.521034910 0.61551840 1.00000000     0.09150144
## wchrt_Baseline   0.105940753 0.109657195 0.09526343 0.09150144     1.00000000
## wchrt_Y1         0.074114430 0.080570086 0.06212365 0.07248302     0.68773094
## wchrt_Y2         0.086126974 0.092143054 0.10225210 0.10149756     0.69955142
## wchrt_Y3         0.099129687 0.082958874 0.14614328 0.14494450     0.61353884
## pubt_Baseline    0.067202313 0.072375380 0.08644283 0.07062126     0.18874495
## pubt_Y1          0.043722404 0.077045354 0.10684269 0.10832306     0.12798975
## pubt_Y2          0.029214014 0.018085413 0.08732790 0.09396024     0.16537334
## pubt_Y3          0.003475505 0.005261589 0.05557784 0.08932391     0.13445550
##                  wchrt_Y1   wchrt_Y2   wchrt_Y3 pubt_Baseline    pubt_Y1
## intt_Baseline  0.07411443 0.08612697 0.09912969    0.06720231 0.04372240
## intt_Y1        0.08057009 0.09214305 0.08295887    0.07237538 0.07704535
## intt_Y2        0.06212365 0.10225210 0.14614328    0.08644283 0.10684269
## intt_Y3        0.07248302 0.10149756 0.14494450    0.07062126 0.10832306
## wchrt_Baseline 0.68773094 0.69955142 0.61353884    0.18874495 0.12798975
## wchrt_Y1       1.00000000 0.69334961 0.68076633    0.18559341 0.15488544
## wchrt_Y2       0.69334961 1.00000000 0.77075601    0.19604711 0.19499036
## wchrt_Y3       0.68076633 0.77075601 1.00000000    0.19078156 0.18733246
## pubt_Baseline  0.18559341 0.19604711 0.19078156    1.00000000 0.46338874
## pubt_Y1        0.15488544 0.19499036 0.18733246    0.46338874 1.00000000
## pubt_Y2        0.15280124 0.18959174 0.24251300    0.34311227 0.57353711
## pubt_Y3        0.12861559 0.15826707 0.18581825    0.24355756 0.44338060
##                   pubt_Y2     pubt_Y3
## intt_Baseline  0.02921401 0.003475505
## intt_Y1        0.01808541 0.005261589
## intt_Y2        0.08732790 0.055577840
## intt_Y3        0.09396024 0.089323913
## wchrt_Baseline 0.16537334 0.134455498
## wchrt_Y1       0.15280124 0.128615590
## wchrt_Y2       0.18959174 0.158267074
## wchrt_Y3       0.24251300 0.185818250
## pubt_Baseline  0.34311227 0.243557557
## pubt_Y1        0.57353711 0.443380600
## pubt_Y2        1.00000000 0.561569185
## pubt_Y3        0.56156918 1.000000000

# Create a ggheatmap
ggheatmap <- ggplot(melt(cor_matrix), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Create a ggheatmap for age regressed variables
ggheatmap <- ggplot(melt(cor_matrix_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 3) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

# Correlation matrix with covariates
# Select the variables for age regressed and covariates
allt_cov_variables <- c("intt_Baseline", "intt_Y1", "intt_Y2", "intt_Y3","intt_Baseline", "wchrt_Baseline", "wchrt_Y1", "wchrt_Y2", "wchrt_Y3","pubt_Baseline", "pubt_Y1", "pubt_Y2", "pubt_Y3", "int_p_ave", "famc_ave", "bw_lbs", "matage", "matalc_ave", "matcig_ave", "matmar_ave", "ses_lt")

# Subset the data for the selected t variables
allt_cov_data <- data_frame %>%
  select(all_of(allt_cov_variables))

# Compute the correlation matrix for age regressed vars + covariates
cor_matrix_cov_t <- cor(allt_cov_data, use = "pairwise.complete.obs")
cor_matrix_cov_t

##                intt_Baseline      intt_Y1     intt_Y2     intt_Y3
## intt_Baseline    1.000000000  0.630156041  0.52360544  0.43398938
## intt_Y1          0.630156041  1.000000000  0.60072899  0.52103491
## intt_Y2          0.523605440  0.600728992  1.00000000  0.61551840
## intt_Y3          0.433989378  0.521034910  0.61551840  1.00000000
## wchrt_Baseline   0.105940753  0.109657195  0.09526343  0.09150144
## wchrt_Y1         0.074114430  0.080570086  0.06212365  0.07248302
## wchrt_Y2         0.086126974  0.092143054  0.10225210  0.10149756
## wchrt_Y3         0.099129687  0.082958874  0.14614328  0.14494450
## pubt_Baseline    0.067202313  0.072375380  0.08644283  0.07062126
## pubt_Y1          0.043722404  0.077045354  0.10684269  0.10832306
## pubt_Y2          0.029214014  0.018085413  0.08732790  0.09396024
## pubt_Y3          0.003475505  0.005261589  0.05557784  0.08932391
## int_p_ave        0.364357470  0.374932706  0.43735274  0.33937486
## famc_ave         0.171589197  0.179936033  0.19711306  0.20711338
## bw_lbs          -0.001175679  0.002893620  0.02063425  0.03825489
## matage          -0.102718436 -0.076087353 -0.04501843 -0.02029135
## matalc_ave       0.058322610  0.001763609  0.06017958  0.01933893
## matcig_ave       0.082429791  0.076840869  0.08092605  0.06714336
## matmar_ave       0.067370984  0.049705393  0.05650990  0.03617843
## ses_lt          -0.252357578 -0.226078211 -0.21536207 -0.16909885
##                wchrt_Baseline     wchrt_Y1     wchrt_Y2     wchrt_Y3
## intt_Baseline     0.105940753  0.074114430  0.086126974  0.099129687
## intt_Y1           0.109657195  0.080570086  0.092143054  0.082958874
## intt_Y2           0.095263426  0.062123652  0.102252100  0.146143279
## intt_Y3           0.091501444  0.072483023  0.101497559  0.144944504
## wchrt_Baseline    1.000000000  0.687730943  0.699551424  0.613538842
## wchrt_Y1          0.687730943  1.000000000  0.693349613  0.680766334
## wchrt_Y2          0.699551424  0.693349613  1.000000000  0.770756010
## wchrt_Y3          0.613538842  0.680766334  0.770756010  1.000000000
## pubt_Baseline     0.188744953  0.185593414  0.196047113  0.190781561
## pubt_Y1           0.127989752  0.154885435  0.194990360  0.187332460
## pubt_Y2           0.165373338  0.152801236  0.189591739  0.242513005
## pubt_Y3           0.134455498  0.128615590  0.158267074  0.185818250
## int_p_ave         0.045365277  0.054395603  0.053764225  0.103004712
## famc_ave          0.007981607 -0.000289402  0.005860146  0.042467646
## bw_lbs            0.083393178  0.059053837  0.045280626  0.059989915
## matage           -0.108358903 -0.113468780 -0.161692951 -0.195410327
## matalc_ave        0.020911880  0.009641091  0.008752588 -0.047163647
## matcig_ave        0.085390681  0.060934928  0.087513087  0.252788177
## matmar_ave        0.050170891  0.039689510  0.070870741  0.007549731
## ses_lt           -0.279389791 -0.246147173 -0.331133704 -0.347660267
##                pubt_Baseline     pubt_Y1     pubt_Y2      pubt_Y3   int_p_ave
## intt_Baseline    0.067202313  0.04372240  0.02921401  0.003475505  0.36435747
## intt_Y1          0.072375380  0.07704535  0.01808541  0.005261589  0.37493271
## intt_Y2          0.086442827  0.10684269  0.08732790  0.055577840  0.43735274
## intt_Y3          0.070621261  0.10832306  0.09396024  0.089323913  0.33937486
## wchrt_Baseline   0.188744953  0.12798975  0.16537334  0.134455498  0.04536528
## wchrt_Y1         0.185593414  0.15488544  0.15280124  0.128615590  0.05439560
## wchrt_Y2         0.196047113  0.19499036  0.18959174  0.158267074  0.05376422
## wchrt_Y3         0.190781561  0.18733246  0.24251300  0.185818250  0.10300471
## pubt_Baseline    1.000000000  0.46338874  0.34311227  0.243557557  0.06490699
## pubt_Y1          0.463388739  1.00000000  0.57353711  0.443380600  0.02706675
## pubt_Y2          0.343112270  0.57353711  1.00000000  0.561569185  0.03167827
## pubt_Y3          0.243557557  0.44338060  0.56156918  1.000000000  0.01438374
## int_p_ave        0.064906995  0.02706675  0.03167827  0.014383740  1.00000000
## famc_ave        -0.027050047 -0.03759675 -0.02268188 -0.047417032  0.33069219
## bw_lbs          -0.002937238  0.01844125 -0.02154450  0.004815945  0.03583271
## matage          -0.158907175 -0.08056884 -0.10221907 -0.082201357 -0.04142178
## matalc_ave      -0.003824003 -0.00656223  0.02348699  0.006002508  0.05125313
## matcig_ave       0.069372283  0.06320936  0.06180227  0.035486193  0.09979529
## matmar_ave       0.032518036  0.05262083  0.03929451  0.022943287  0.08777126
## ses_lt          -0.228204452 -0.20254816 -0.18224390 -0.138791809 -0.30098071
##                    famc_ave       bw_lbs       matage   matalc_ave  matcig_ave
## intt_Baseline   0.171589197 -0.001175679 -0.102718436  0.058322610  0.08242979
## intt_Y1         0.179936033  0.002893620 -0.076087353  0.001763609  0.07684087
## intt_Y2         0.197113056  0.020634250 -0.045018429  0.060179578  0.08092605
## intt_Y3         0.207113378  0.038254890 -0.020291353  0.019338933  0.06714336
## wchrt_Baseline  0.007981607  0.083393178 -0.108358903  0.020911880  0.08539068
## wchrt_Y1       -0.000289402  0.059053837 -0.113468780  0.009641091  0.06093493
## wchrt_Y2        0.005860146  0.045280626 -0.161692951  0.008752588  0.08751309
## wchrt_Y3        0.042467646  0.059989915 -0.195410327 -0.047163647  0.25278818
## pubt_Baseline  -0.027050047 -0.002937238 -0.158907175 -0.003824003  0.06937228
## pubt_Y1        -0.037596748  0.018441249 -0.080568839 -0.006562230  0.06320936
## pubt_Y2        -0.022681878 -0.021544501 -0.102219067  0.023486991  0.06180227
## pubt_Y3        -0.047417032  0.004815945 -0.082201357  0.006002508  0.03548619
## int_p_ave       0.330692190  0.035832715 -0.041421784  0.051253132  0.09979529
## famc_ave        1.000000000  0.011813744  0.011197830  0.040081117  0.04386867
## bw_lbs          0.011813744  1.000000000 -0.003120232  0.006500121 -0.04214129
## matage          0.011197830 -0.003120232  1.000000000  0.033601539 -0.06339791
## matalc_ave      0.040081117  0.006500121  0.033601539  1.000000000  0.19389421
## matcig_ave      0.043868672 -0.042141294 -0.063397912  0.193894211  1.00000000
## matmar_ave      0.029964344 -0.009808363 -0.086547582  0.071259864  0.13319494
## ses_lt         -0.099308103  0.039716175  0.509444691 -0.007411927 -0.22344928
##                  matmar_ave       ses_lt
## intt_Baseline   0.067370984 -0.252357578
## intt_Y1         0.049705393 -0.226078211
## intt_Y2         0.056509897 -0.215362074
## intt_Y3         0.036178429 -0.169098853
## wchrt_Baseline  0.050170891 -0.279389791
## wchrt_Y1        0.039689510 -0.246147173
## wchrt_Y2        0.070870741 -0.331133704
## wchrt_Y3        0.007549731 -0.347660267
## pubt_Baseline   0.032518036 -0.228204452
## pubt_Y1         0.052620830 -0.202548163
## pubt_Y2         0.039294512 -0.182243903
## pubt_Y3         0.022943287 -0.138791809
## int_p_ave       0.087771261 -0.300980711
## famc_ave        0.029964344 -0.099308103
## bw_lbs         -0.009808363  0.039716175
## matage         -0.086547582  0.509444691
## matalc_ave      0.071259864 -0.007411927
## matcig_ave      0.133194945 -0.223449280
## matmar_ave      1.000000000 -0.156379966
## ses_lt         -0.156379966  1.000000000

# Create a ggheatmap for age regressed variables + covariates
ggheatmap <- ggplot(melt(cor_matrix_cov_t), aes(Var2, Var1, fill = value)) +
  geom_tile(color = "white") +
  scale_fill_gradient2(low = "black", high = "#8e6f3e", mid = "white",
                       midpoint = 0, limit = c(-1, 1), space = "Lab",
                       name = "Pearson\nCorrelation") +
  theme_minimal() +  # minimal theme
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 12, hjust = 1)) +
  coord_fixed()

# Create a ggheatmap with labels on the lower triangle
ggheatmap +
  geom_text(aes(Var1, Var2, label = ifelse(as.numeric(Var1) > as.numeric(Var2), round(value, 2), "")),
            color = "black", size = 2) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank(),
    axis.ticks = element_blank(),
    legend.justification = c(1, 0),
    legend.position = c(1.3, 0.1),
    legend.direction = "vertical"
  ) +
  guides(fill = guide_colorbar(barwidth = 1.3, barheight = 6,
                               title.position = "top", title.hjust = 0.5)) +
  coord_fixed() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Export to Mplus

# Subset data set for mplus
all_merged_out <- all_merged[, c("sex","race3", "age_Baseline", 
                           "int_Baseline", "intt_Baseline",
                           "age_Y1", "int_Y1", "intt_Y1",
                           "age_Y2", "int_Y2", "intt_Y2",
                           "age_Y3", "int_Y3", "intt_Y3",
                           "wchr_Baseline", "wchrt_Baseline",
                           "wchr_Y1", "wchrt_Y1",
                           "wchr_Y2", "wchrt_Y2",
                           "wchr_Y3", "wchrt_Y3",
                           "pub_Baseline", "pubt_Baseline",
                           "pub_Y1", "pubt_Y1",
                           "pub_Y2", "pubt_Y2",
                           "pub_Y3", "pubt_Y3",
                           "int_p_ave", "famc_ave", "bw_lbs",
                           "matage", "matalc_ave", "matcig_ave",
                           "matmar_ave", "ses_lt")]

#install.packages("MplusAutomation")
library(MplusAutomation)

## Warning: package 'MplusAutomation' was built under R version 4.3.3

## Version:  1.1.1
## We work hard to write this free software. Please help us get credit by citing: 
## 
## Hallquist, M. N. & Wiley, J. F. (2018). MplusAutomation: An R Package for Facilitating Large-Scale Latent Variable Analyses in Mplus. Structural Equation Modeling, 25, 621-638. doi: 10.1080/10705511.2017.1402334.
## 
## -- see citation("MplusAutomation").

# Specify the output Mplus data file name (e.g., "data_input.dat")
mplus_data_file <- "data_input.dat"

# Export data to Mplus input format
MplusAutomation::prepareMplusData(all_merged_out,filename = "Fullsample_race3_sex_subset.dat")

## The file(s)
##  'Fullsample_race3_sex_subset.dat' 
## currently exist(s) and will be overwritten

## TITLE: Your title goes here
## DATA: FILE = "Fullsample_race3_sex_subset.dat";
## VARIABLE: 
## NAMES = sex race3 age_Baseline int_Baseline intt_Baseline age_Y1 int_Y1 intt_Y1
##      age_Y2 int_Y2 intt_Y2 age_Y3 int_Y3 intt_Y3 wchr_Baseline wchrt_Baseline
##      wchr_Y1 wchrt_Y1 wchr_Y2 wchrt_Y2 wchr_Y3 wchrt_Y3 pub_Baseline pubt_Baseline
##      pub_Y1 pubt_Y1 pub_Y2 pubt_Y2 pub_Y3 pubt_Y3 int_p_ave famc_ave bw_lbs matage
##      matalc_ave matcig_ave matmar_ave ses_lt; 
## MISSING=.;

Hallquist, M. N. & Wiley, J. F. (2018). MplusAutomation: An R Package for Facilitating Large-Scale Latent Variable Analyses in Mplus. Structural Equation Modeling, 25, 621-638. doi: 10.1080/10705511.2017.1402334.

Model Building

Internalizing

Internalizing Unconstrained model

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/internalizing unconstrained.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024  11:59 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Internalizing Constrained Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   intt_b intt_1
##   intt_2 intt_3;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   ! Estimate the Lagged Effects
##   wintt_1 ON wintt_b;
##   wintt_2 ON wintt_1;
##   wintt_3 ON wintt_2;
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_intt with wintt_b@0;
## 
##   OUTPUT: STDYX MODINDICES;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2095
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Internalizing Constrained Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10361
## 
## Number of dependent variables                                    4
## Number of independent variables                                  0
## Number of continuous latent variables                            5
## 
## Observed dependent variables
## 
##   Continuous
##    INTT_B      INTT_1      INTT_2      INTT_3
## 
## Continuous latent variables
##    RI_INTT     WINTT_B     WINTT_1     WINTT_2     WINTT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns            12
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               INTT_B        INTT_1        INTT_2        INTT_3
##               ________      ________      ________      ________
##  INTT_B         0.999
##  INTT_1         0.943         0.944
##  INTT_2         0.918         0.897         0.919
##  INTT_3         0.851         0.833         0.834         0.851
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      INTT_B                0.000       2.512      -1.161    0.27%      -1.096     -0.934     -0.912
##            10355.000       2.893       8.153      13.915    0.01%      -0.129      0.904
##      INTT_1                0.000       2.416      -1.298    0.01%      -1.130     -1.052     -0.986
##             9780.000       3.147       7.265      12.912    0.01%      -0.139      0.905
##      INTT_2                0.000       2.363      -1.697    0.01%      -1.274     -1.119     -1.024
##             9519.000       3.840       7.067      15.034    0.01%      -0.293      0.867
##      INTT_3                0.000       2.123      -1.822    0.02%      -1.459     -1.307     -0.672
##             8819.000       4.614       5.379      13.693    0.01%      -0.398      1.370
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       12
## 
## Loglikelihood
## 
##           H0 Value                      -71300.350
##           H0 Scaling Correction Factor      2.8090
##             for MLR
##           H1 Value                      -71257.871
##           H1 Scaling Correction Factor      2.7385
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  142624.700
##           Bayesian (BIC)                142711.649
##           Sample-Size Adjusted BIC      142673.515
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                             36.694*
##           Degrees of Freedom                     2
##           P-Value                           0.0000
##           Scaling Correction Factor         2.3153
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.041
##           90 Percent C.I.                    0.030  0.053
##           Probability RMSEA <= .05           0.888
## 
## CFI/TLI
## 
##           CFI                                0.994
##           TLI                                0.981
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           5547.969
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.016
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WINTT_1  ON
##     WINTT_B            0.053      0.047      1.130      0.259
## 
##  WINTT_2  ON
##     WINTT_1            0.230      0.037      6.285      0.000
## 
##  WINTT_3  ON
##     WINTT_2            0.427      0.026     16.718      0.000
## 
##  RI_INTT  WITH
##     WINTT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     INTT_B             0.001      0.017      0.041      0.967
##     INTT_1             0.008      0.018      0.475      0.635
##     INTT_2             0.010      0.020      0.496      0.620
##     INTT_3             0.024      0.023      1.056      0.291
## 
##  Variances
##     RI_INTT            1.848      0.070     26.366      0.000
##     WINTT_B            1.113      0.066     16.749      0.000
## 
##  Residual Variances
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.231      0.075     16.493      0.000
##     WINTT_2            1.958      0.076     25.677      0.000
##     WINTT_3            2.463      0.079     31.047      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.318E-01
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.790      0.011     73.106      0.000
##     INTT_1             0.774      0.013     60.711      0.000
##     INTT_2             0.691      0.010     67.973      0.000
##     INTT_3             0.628      0.010     63.799      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.613      0.014     44.024      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.633      0.016     40.539      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.723      0.010     74.450      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.778      0.008     97.788      0.000
## 
##  WINTT_1  ON
##     WINTT_B            0.050      0.044      1.138      0.255
## 
##  WINTT_2  ON
##     WINTT_1            0.179      0.030      5.992      0.000
## 
##  WINTT_3  ON
##     WINTT_2            0.361      0.021     17.576      0.000
## 
##  RI_INTT  WITH
##     WINTT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     INTT_B             0.000      0.010      0.041      0.967
##     INTT_1             0.005      0.010      0.478      0.633
##     INTT_2             0.005      0.010      0.499      0.618
##     INTT_3             0.011      0.010      1.067      0.286
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.997      0.004    225.603      0.000
##     WINTT_2            0.968      0.011     90.006      0.000
##     WINTT_3            0.870      0.015     58.703      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.003      0.004      0.569      0.569
##     WINTT_2            0.032      0.011      2.996      0.003
##     WINTT_3            0.130      0.015      8.788      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_INTT  BY INTT_B                32.952    -0.236     -0.321       -0.187
## RI_INTT  BY INTT_1                28.314     0.175      0.238        0.135
## WINTT_B  BY INTT_3                23.596    -0.174     -0.183       -0.085
## WINTT_1  BY INTT_2                32.940    -0.443     -0.492       -0.250
## WINTT_1  BY INTT_3                33.005     0.189      0.210        0.097
## WINTT_3  BY INTT_B                30.408    -0.095     -0.159       -0.093
## WINTT_3  BY INTT_1                33.506     0.089      0.150        0.086
## WINTT_3  BY INTT_2                33.057    -0.656     -1.103       -0.561
## 
## ON/BY Statements
## 
## RI_INTT  ON WINTT_B  /
## WINTT_B  BY RI_INTT               32.943    -0.417     -0.324       -0.324
## RI_INTT  ON WINTT_1  /
## WINTT_1  BY RI_INTT               33.096     0.331      0.270        0.270
## WINTT_B  ON RI_INTT  /
## RI_INTT  BY WINTT_B               32.943    -0.251     -0.324       -0.324
## WINTT_B  ON WINTT_3  /
## WINTT_3  BY WINTT_B               29.463    -0.098     -0.156       -0.156
## WINTT_1  ON RI_INTT  /
## RI_INTT  BY WINTT_1               33.090     0.212      0.259        0.259
## WINTT_1  ON WINTT_3  /
## WINTT_3  BY WINTT_1               33.516     0.092      0.140        0.140
## WINTT_2  ON WINTT_3  /
## WINTT_3  BY WINTT_2               33.160    -0.657     -0.777       -0.777
## WINTT_3  ON WINTT_B  /
## WINTT_B  BY WINTT_3               23.596    -0.174     -0.109       -0.109
## WINTT_3  ON WINTT_1  /
## WINTT_1  BY WINTT_3               33.005     0.189      0.125        0.125
## 
## WITH Statements
## 
## INTT_2   WITH INTT_1              34.466    -0.532     -0.532      999.000
## INTT_3   WITH INTT_B              24.903    -0.192     -0.192      999.000
## INTT_3   WITH INTT_1              33.641     0.221      0.221      999.000
## INTT_3   WITH INTT_2              32.835    -1.610     -1.610      999.000
## WINTT_B  WITH RI_INTT             32.943    -0.464     -0.324       -0.324
## WINTT_1  WITH RI_INTT             33.090     0.391      0.259        0.259
## WINTT_3  WITH WINTT_B             23.596    -0.193     -0.117       -0.117
## WINTT_3  WITH WINTT_1             33.662     0.228      0.131        0.131
## WINTT_3  WITH WINTT_2             32.945    -1.612     -0.734       -0.734
## 
## Variances/Residual Variances
## 
## INTT_2                            32.124     3.730      3.730        0.963
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\internalizing unconstrained.dgm
## 
##      Beginning Time:  11:59:19
##         Ending Time:  11:59:19
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Internalizing Constrained model

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/internalizing constrained.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024  11:50 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Internalizing Constrained Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   intt_b intt_1
##   intt_2 intt_3;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   ! Estimate the Lagged Effects
##   wintt_1 ON wintt_b (1);
##   wintt_2 ON wintt_1 (1);
##   wintt_3 ON wintt_2 (1);
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_intt with wintt_b@0;
## 
##   OUTPUT: STDYX MODINDICES;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2095
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Internalizing Constrained Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10361
## 
## Number of dependent variables                                    4
## Number of independent variables                                  0
## Number of continuous latent variables                            5
## 
## Observed dependent variables
## 
##   Continuous
##    INTT_B      INTT_1      INTT_2      INTT_3
## 
## Continuous latent variables
##    RI_INTT     WINTT_B     WINTT_1     WINTT_2     WINTT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns            12
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               INTT_B        INTT_1        INTT_2        INTT_3
##               ________      ________      ________      ________
##  INTT_B         0.999
##  INTT_1         0.943         0.944
##  INTT_2         0.918         0.897         0.919
##  INTT_3         0.851         0.833         0.834         0.851
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      INTT_B                0.000       2.512      -1.161    0.27%      -1.096     -0.934     -0.912
##            10355.000       2.893       8.153      13.915    0.01%      -0.129      0.904
##      INTT_1                0.000       2.416      -1.298    0.01%      -1.130     -1.052     -0.986
##             9780.000       3.147       7.265      12.912    0.01%      -0.139      0.905
##      INTT_2                0.000       2.363      -1.697    0.01%      -1.274     -1.119     -1.024
##             9519.000       3.840       7.067      15.034    0.01%      -0.293      0.867
##      INTT_3                0.000       2.123      -1.822    0.02%      -1.459     -1.307     -0.672
##             8819.000       4.614       5.379      13.693    0.01%      -0.398      1.370
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       10
## 
## Loglikelihood
## 
##           H0 Value                      -71389.816
##           H0 Scaling Correction Factor      2.8983
##             for MLR
##           H1 Value                      -71257.871
##           H1 Scaling Correction Factor      2.7385
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  142799.631
##           Bayesian (BIC)                142872.089
##           Sample-Size Adjusted BIC      142840.311
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                            112.830*
##           Degrees of Freedom                     4
##           P-Value                           0.0000
##           Scaling Correction Factor         2.3388
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.051
##           90 Percent C.I.                    0.043  0.060
##           Probability RMSEA <= .05           0.383
## 
## CFI/TLI
## 
##           CFI                                0.980
##           TLI                                0.971
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           5547.969
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.038
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WINTT_1  ON
##     WINTT_B            0.317      0.029     11.042      0.000
## 
##  WINTT_2  ON
##     WINTT_1            0.317      0.029     11.042      0.000
## 
##  WINTT_3  ON
##     WINTT_2            0.317      0.029     11.042      0.000
## 
##  RI_INTT  WITH
##     WINTT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     INTT_B             0.001      0.017      0.042      0.967
##     INTT_1             0.009      0.018      0.516      0.606
##     INTT_2             0.009      0.020      0.473      0.636
##     INTT_3             0.021      0.022      0.951      0.342
## 
##  Variances
##     RI_INTT            1.670      0.072     23.087      0.000
##     WINTT_B            1.349      0.061     21.995      0.000
## 
##  Residual Variances
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.495      0.067     22.388      0.000
##     WINTT_2            1.926      0.078     24.722      0.000
##     WINTT_3            2.392      0.081     29.545      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.399E-01
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.744      0.010     75.559      0.000
##     INTT_1             0.711      0.014     52.098      0.000
##     INTT_2             0.666      0.014     48.870      0.000
##     INTT_3             0.625      0.013     49.313      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.668      0.011     61.009      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.703      0.014     50.851      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.746      0.012     61.156      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.780      0.010     76.821      0.000
## 
##  WINTT_1  ON
##     WINTT_B            0.288      0.021     13.799      0.000
## 
##  WINTT_2  ON
##     WINTT_1            0.280      0.027     10.374      0.000
## 
##  WINTT_3  ON
##     WINTT_2            0.284      0.028     10.275      0.000
## 
##  RI_INTT  WITH
##     WINTT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     INTT_B             0.000      0.010      0.042      0.967
##     INTT_1             0.005      0.010      0.519      0.604
##     INTT_2             0.005      0.010      0.476      0.634
##     INTT_3             0.010      0.011      0.959      0.337
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.917      0.012     76.105      0.000
##     WINTT_2            0.922      0.015     60.995      0.000
##     WINTT_3            0.919      0.016     58.509      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.083      0.012      6.899      0.000
##     WINTT_2            0.078      0.015      5.187      0.000
##     WINTT_3            0.081      0.016      5.137      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_INTT  BY INTT_B                40.049    -0.215     -0.278       -0.160
## RI_INTT  BY INTT_3                28.640     0.143      0.185        0.090
## WINTT_B  BY INTT_B                39.577     0.592      0.688        0.396
## WINTT_B  BY INTT_1                43.522    -0.182     -0.211       -0.116
## WINTT_B  BY INTT_2                14.157     0.110      0.128        0.066
## WINTT_B  BY INTT_3                18.145    -0.151     -0.175       -0.085
## WINTT_1  BY INTT_B                39.574    -0.186     -0.238       -0.137
## WINTT_1  BY INTT_3                70.636     0.236      0.301        0.146
## WINTT_2  BY INTT_2                17.602    -0.194     -0.280       -0.144
## WINTT_2  BY INTT_3                53.146     0.214      0.309        0.149
## WINTT_3  BY INTT_B                41.351    -0.116     -0.187       -0.108
## WINTT_3  BY INTT_1                44.163     0.099      0.160        0.088
## WINTT_3  BY INTT_2                22.452     0.139      0.223        0.115
## WINTT_3  BY INTT_3                53.683     0.678      1.093        0.529
## 
## ON/BY Statements
## 
## RI_INTT  ON WINTT_B  /
## WINTT_B  BY RI_INTT               67.105    -0.409     -0.367       -0.367
## RI_INTT  ON WINTT_2  /
## WINTT_2  BY RI_INTT               12.525     0.087      0.097        0.097
## RI_INTT  ON WINTT_3  /
## WINTT_3  BY RI_INTT               43.517     0.131      0.164        0.164
## WINTT_B  ON RI_INTT  /
## RI_INTT  BY WINTT_B               67.105    -0.330     -0.367       -0.367
## WINTT_B  ON WINTT_1  /
## WINTT_1  BY WINTT_B               39.588    -0.169     -0.186       -0.186
## WINTT_B  ON WINTT_3  /
## WINTT_3  BY WINTT_B               22.236    -0.114     -0.158       -0.158
## WINTT_1  ON WINTT_B  /
## WINTT_B  BY WINTT_1               39.587    -0.145     -0.132       -0.132
## WINTT_1  ON WINTT_1  /
## WINTT_1  BY WINTT_1               39.730    -0.594     -0.594       -0.594
## WINTT_1  ON WINTT_3  /
## WINTT_3  BY WINTT_1               62.616     0.124      0.156        0.156
## WINTT_2  ON RI_INTT  /
## RI_INTT  BY WINTT_2               14.523     0.095      0.085        0.085
## WINTT_2  ON WINTT_B  /
## WINTT_B  BY WINTT_2               10.951     0.121      0.097        0.097
## WINTT_2  ON WINTT_3  /
## WINTT_3  BY WINTT_2               25.043     0.134      0.149        0.149
## WINTT_3  ON RI_INTT  /
## RI_INTT  BY WINTT_3               28.640     0.143      0.115        0.115
## WINTT_3  ON WINTT_B  /
## WINTT_B  BY WINTT_3               18.145    -0.151     -0.109       -0.109
## WINTT_3  ON WINTT_1  /
## WINTT_1  BY WINTT_3               70.636     0.236      0.187        0.187
## WINTT_3  ON WINTT_2  /
## WINTT_2  BY WINTT_3               53.146     0.092      0.082        0.082
## WINTT_3  ON WINTT_3  /
## WINTT_3  BY WINTT_3               53.683     0.678      0.678        0.678
## 
## WITH Statements
## 
## INTT_1   WITH INTT_B              50.030    -0.275     -0.275      999.000
## INTT_2   WITH INTT_B              19.911     0.150      0.150      999.000
## INTT_2   WITH INTT_1              13.686    -0.127     -0.127      999.000
## INTT_3   WITH INTT_B              37.309    -0.232     -0.232      999.000
## INTT_3   WITH INTT_1              55.236     0.276      0.276      999.000
## INTT_3   WITH INTT_2              22.758     0.285      0.285      999.000
## WINTT_B  WITH RI_INTT             67.105    -0.551     -0.367       -0.367
## WINTT_1  WITH WINTT_B             39.587    -0.253     -0.178       -0.178
## WINTT_2  WITH RI_INTT             14.523     0.159      0.089        0.089
## WINTT_2  WITH WINTT_B             10.951     0.163      0.101        0.101
## WINTT_3  WITH RI_INTT             28.640     0.239      0.120        0.120
## WINTT_3  WITH WINTT_B             18.145    -0.203     -0.113       -0.113
## WINTT_3  WITH WINTT_1             73.031     0.324      0.171        0.171
## WINTT_3  WITH WINTT_2             22.789     0.285      0.133        0.133
## 
## Variances/Residual Variances
## 
## INTT_B                            39.576     0.799      0.799        0.265
## INTT_2                            22.826    -0.901     -0.901       -0.240
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\internalizing constrained.dgm
## 
##      Beginning Time:  11:50:55
##         Ending Time:  11:50:55
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Loglikelihood test for Internalizing

https://www.statmodel.com/chidiff.shtml

#install.packages("stats")
library(stats)

# Number of Free Parameters                       12
# Loglikelihood
#          H0 Value                      -71300.350
#          H0 Scaling Correction Factor      2.8090
#            for MLR
#          H1 Value                      -71257.871
#          H1 Scaling Correction Factor      2.7385
#            for MLR

# Unconstrained
L1 <- -71300.350  # Loglikelihood for the H1 model
c1 <- 2.8090  # Scaling correction factor for the H1 model
p1 <- 12     # Number of parameters for the H1 model

# Number of Free Parameters                       10
# Loglikelihood
#          H0 Value                      -71389.816
#          H0 Scaling Correction Factor      2.8983
#            for MLR
#          H1 Value                      -71257.871
#          H1 Scaling Correction Factor      2.7385
#            for MLR

# Constrained
L0 <- -71389.816  # Loglikelihood for the H0 model
c0 <- 2.8983  # Scaling correction factor for the H0 model
p0 <- 10    # Number of parameters for the H0 model

# Compute the difference test scaling correction (cd)
cd <- (p0 * c0 - p1 * c1) / (p0 - p1)

# Compute the chi-square difference test (TRd)
TRd <- -2 * (L0 - L1) / cd

# Define degrees of freedom
df <- p1 - p0

# Calculate p-value
p_value <- pchisq(TRd, df = df, lower.tail = FALSE)

# Print results
cat("Difference Test Scaling Correction (cd):", cd, "\n")

## Difference Test Scaling Correction (cd): 2.3625

cat("Chi-Square Difference Test (TRd):", TRd, "\n")

## Chi-Square Difference Test (TRd): 75.73841

cat("p-value:", p_value, "\n")

## p-value: 3.577772e-17

# Print "Cannot constrain" if p-value is less than 0.05
if (p_value < 0.05) {
  cat("Cannot constrain\n")
} else {
  cat("Constraining is acceptable\n")
}

## Cannot constrain

Waist Circumference to Height Ratio

Waist Circumference to Height Ratio Unconstrained model

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/wchr unconstrained.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024  12:36 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Waist Circumference to Height Ratio Unconstrained Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random wchrtercept)
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! Create within-person centered variables
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b;
##   wwchrt_2 ON wwchrt_1;
##   wwchrt_3 ON wwchrt_2;
## 
##   ! Constrain the measurement error variances to zero
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   ! ask for variances for all variables that are included;
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0;
## 
##   OUTPUT: STDYX MODINDICES;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2095
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Waist Circumference to Height Ratio Unconstrained Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10361
## 
## Number of dependent variables                                    4
## Number of independent variables                                  0
## Number of continuous latent variables                            5
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3
## 
## Continuous latent variables
##    RI_WCHRT    WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns            13
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3
##               ________      ________      ________      ________
##  WCHRT_B        0.998
##  WCHRT_1        0.936         0.937
##  WCHRT_2        0.763         0.746         0.764
##  WCHRT_3        0.169         0.166         0.153         0.169
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B               0.000       1.308      -0.241    0.01%      -0.055     -0.029     -0.014
##            10342.000       0.005       4.917       0.891    0.01%       0.002      0.051
##      WCHRT_1               0.000       2.054      -0.213    0.01%      -0.058     -0.031     -0.016
##             9711.000       0.006      13.985       0.997    0.01%       0.001      0.054
##      WCHRT_2               0.000       1.516      -0.220    0.01%      -0.062     -0.033     -0.017
##             7917.000       0.006       6.773       0.922    0.01%       0.002      0.056
##      WCHRT_3               0.000       1.723      -0.149    0.06%      -0.068     -0.038     -0.022
##             1754.000       0.007       7.313       0.770    0.06%      -0.001      0.064
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       12
## 
## Loglikelihood
## 
##           H0 Value                       42900.924
##           H0 Scaling Correction Factor      8.5361
##             for MLR
##           H1 Value                       42910.217
##           H1 Scaling Correction Factor      7.7273
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  -85777.849
##           Bayesian (BIC)                -85690.899
##           Sample-Size Adjusted BIC      -85729.033
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                              6.465*
##           Degrees of Freedom                     2
##           P-Value                           0.0395
##           Scaling Correction Factor         2.8748
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.015
##           90 Percent C.I.                    0.003  0.028
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.996
##           TLI                                0.988
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           1123.303
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.010
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.114      0.070     -1.628      0.104
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.200      0.039      5.166      0.000
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.494      0.078      6.337      0.000
## 
##  RI_WCHRT WITH
##     WWCHRT_B           0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.001      0.038      0.969
##     WCHRT_1            0.001      0.001      0.696      0.486
##     WCHRT_2            0.002      0.001      1.939      0.053
##     WCHRT_3           -0.007      0.001     -5.158      0.000
## 
##  Variances
##     RI_WCHRT           0.004      0.000     40.241      0.000
##     WWCHRT_B           0.001      0.000      8.782      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     WWCHRT_1           0.002      0.000      7.539      0.000
##     WWCHRT_2           0.002      0.000     12.647      0.000
##     WWCHRT_3           0.002      0.000      6.482      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.185E-06
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_WCHRT BY
##     WCHRT_B            0.891      0.011     78.966      0.000
##     WCHRT_1            0.830      0.018     47.341      0.000
##     WCHRT_2            0.797      0.012     65.213      0.000
##     WCHRT_3            0.752      0.025     30.468      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.455      0.022     20.560      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.558      0.026     21.439      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.604      0.016     37.548      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.659      0.028     23.386      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.086      0.053     -1.636      0.102
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.178      0.032      5.499      0.000
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.428      0.060      7.117      0.000
## 
##  RI_WCHRT WITH
##     WWCHRT_B           0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.010      0.038      0.969
##     WCHRT_1            0.007      0.010      0.701      0.483
##     WCHRT_2            0.020      0.010      1.970      0.049
##     WCHRT_3           -0.085      0.018     -4.753      0.000
## 
##  Variances
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     WWCHRT_1           0.993      0.009    108.559      0.000
##     WWCHRT_2           0.968      0.011     84.398      0.000
##     WWCHRT_3           0.817      0.051     15.893      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WWCHRT_1           0.007      0.009      0.818      0.413
##     WWCHRT_2           0.032      0.011      2.749      0.006
##     WWCHRT_3           0.183      0.051      3.558      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## No modification indices above the minimum value.
## 
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\wchr unconstrained.dgm
## 
##      Beginning Time:  12:36:16
##         Ending Time:  12:36:16
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Waist Circumference to Height Ratio Constrained model

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/wchr constrained.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024  12:39 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Waist Circumference to Height Ratio Unconstrained Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random wchrtercept)
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! Create within-person centered variables
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b (1);
##   wwchrt_2 ON wwchrt_1 (1);
##   wwchrt_3 ON wwchrt_2 (1);
## 
##   ! Constrain the measurement error variances to zero
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   ! ask for variances for all variables that are included;
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0;
## 
##   OUTPUT: STDYX MODINDICES;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2095
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Waist Circumference to Height Ratio Unconstrained Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10361
## 
## Number of dependent variables                                    4
## Number of independent variables                                  0
## Number of continuous latent variables                            5
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3
## 
## Continuous latent variables
##    RI_WCHRT    WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns            13
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3
##               ________      ________      ________      ________
##  WCHRT_B        0.998
##  WCHRT_1        0.936         0.937
##  WCHRT_2        0.763         0.746         0.764
##  WCHRT_3        0.169         0.166         0.153         0.169
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B               0.000       1.308      -0.241    0.01%      -0.055     -0.029     -0.014
##            10342.000       0.005       4.917       0.891    0.01%       0.002      0.051
##      WCHRT_1               0.000       2.054      -0.213    0.01%      -0.058     -0.031     -0.016
##             9711.000       0.006      13.985       0.997    0.01%       0.001      0.054
##      WCHRT_2               0.000       1.516      -0.220    0.01%      -0.062     -0.033     -0.017
##             7917.000       0.006       6.773       0.922    0.01%       0.002      0.056
##      WCHRT_3               0.000       1.723      -0.149    0.06%      -0.068     -0.038     -0.022
##             1754.000       0.007       7.313       0.770    0.06%      -0.001      0.064
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       10
## 
## Loglikelihood
## 
##           H0 Value                       42844.638
##           H0 Scaling Correction Factor      9.5102
##             for MLR
##           H1 Value                       42910.217
##           H1 Scaling Correction Factor      7.7273
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  -85669.277
##           Bayesian (BIC)                -85596.819
##           Sample-Size Adjusted BIC      -85628.597
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                             40.107*
##           Degrees of Freedom                     4
##           P-Value                           0.0000
##           Scaling Correction Factor         3.2702
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.030
##           90 Percent C.I.                    0.022  0.038
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.968
##           TLI                                0.952
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           1123.303
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.039
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B           0.260      0.041      6.405      0.000
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.260      0.041      6.405      0.000
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.260      0.041      6.405      0.000
## 
##  RI_WCHRT WITH
##     WWCHRT_B           0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.001      0.041      0.967
##     WCHRT_1            0.001      0.001      0.731      0.465
##     WCHRT_2            0.001      0.001      1.772      0.076
##     WCHRT_3           -0.006      0.001     -4.587      0.000
## 
##  Variances
##     RI_WCHRT           0.004      0.000     37.613      0.000
##     WWCHRT_B           0.001      0.000      9.894      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     WWCHRT_1           0.002      0.000     10.401      0.000
##     WWCHRT_2           0.002      0.000     11.570      0.000
##     WWCHRT_3           0.002      0.000      5.880      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.295E-05
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_WCHRT BY
##     WCHRT_B            0.854      0.013     66.688      0.000
##     WCHRT_1            0.783      0.014     54.523      0.000
##     WCHRT_2            0.788      0.015     51.931      0.000
##     WCHRT_3            0.770      0.026     29.339      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.520      0.021     24.683      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.622      0.018     34.467      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.615      0.019     31.647      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.638      0.032     20.151      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B           0.199      0.034      5.853      0.000
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.265      0.039      6.821      0.000
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.245      0.045      5.440      0.000
## 
##  RI_WCHRT WITH
##     WWCHRT_B           0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.010      0.041      0.967
##     WCHRT_1            0.007      0.010      0.736      0.462
##     WCHRT_2            0.019      0.011      1.797      0.072
##     WCHRT_3           -0.082      0.019     -4.235      0.000
## 
##  Variances
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     WWCHRT_1           0.960      0.014     71.035      0.000
##     WWCHRT_2           0.930      0.021     45.244      0.000
##     WWCHRT_3           0.940      0.022     42.644      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WWCHRT_1           0.040      0.014      2.926      0.003
##     WWCHRT_2           0.070      0.021      3.411      0.001
##     WWCHRT_3           0.060      0.022      2.720      0.007
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_WCHRT BY WCHRT_B               10.309    -0.153     -0.009       -0.131
## RI_WCHRT BY WCHRT_1               12.536    -0.078     -0.005       -0.061
## RI_WCHRT BY WCHRT_2               14.382     0.080      0.005        0.063
## WWCHRT_B BY WCHRT_B               12.868     0.756      0.028        0.393
## WWCHRT_B BY WCHRT_1               15.096    -0.190     -0.007       -0.091
## WWCHRT_B BY WCHRT_2               20.040     0.322      0.012        0.154
## WWCHRT_B BY WCHRT_3               10.618    -0.299     -0.011       -0.140
## WWCHRT_1 BY WCHRT_B               12.868    -0.125     -0.006       -0.085
## WWCHRT_1 BY WCHRT_3               11.005     0.194      0.009        0.119
## WWCHRT_2 BY WCHRT_B               11.141     0.195      0.009        0.130
## WWCHRT_2 BY WCHRT_3               16.664     0.265      0.012        0.159
## WWCHRT_3 BY WCHRT_B               11.836    -0.181     -0.009       -0.128
## WWCHRT_3 BY WCHRT_2               10.472     0.206      0.010        0.135
## WWCHRT_3 BY WCHRT_3               16.665     1.020      0.051        0.651
## 
## ON/BY Statements
## 
## RI_WCHRT ON WWCHRT_B /
## WWCHRT_B BY RI_WCHRT              21.358    -0.602     -0.366       -0.366
## RI_WCHRT ON WWCHRT_1 /
## WWCHRT_1 BY RI_WCHRT              12.098    -0.159     -0.126       -0.126
## RI_WCHRT ON WWCHRT_2 /
## WWCHRT_2 BY RI_WCHRT              16.659     0.186      0.146        0.146
## RI_WCHRT ON WWCHRT_3 /
## WWCHRT_3 BY RI_WCHRT              12.556     0.234      0.194        0.194
## WWCHRT_B ON RI_WCHRT /
## RI_WCHRT BY WWCHRT_B              21.358    -0.223     -0.366       -0.366
## WWCHRT_B ON WWCHRT_1 /
## WWCHRT_1 BY WWCHRT_B              12.868    -0.120     -0.157       -0.157
## WWCHRT_B ON WWCHRT_2 /
## WWCHRT_2 BY WWCHRT_B              12.251     0.230      0.295        0.295
## WWCHRT_1 ON WWCHRT_B /
## WWCHRT_B BY WWCHRT_1              12.868    -0.191     -0.146       -0.146
## WWCHRT_1 ON WWCHRT_1 /
## WWCHRT_1 BY WWCHRT_1              12.868    -0.756     -0.756       -0.756
## WWCHRT_1 ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_1              10.520     0.159      0.165        0.165
## WWCHRT_2 ON RI_WCHRT /
## RI_WCHRT BY WWCHRT_2              17.274     0.090      0.115        0.115
## WWCHRT_2 ON WWCHRT_B /
## WWCHRT_B BY WWCHRT_2              18.626     0.351      0.274        0.274
## WWCHRT_2 ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_2              10.879     0.198      0.210        0.210
## WWCHRT_3 ON WWCHRT_B /
## WWCHRT_B BY WWCHRT_3              10.618    -0.299     -0.219       -0.219
## WWCHRT_3 ON WWCHRT_1 /
## WWCHRT_1 BY WWCHRT_3              11.005     0.194      0.186        0.186
## WWCHRT_3 ON WWCHRT_2 /
## WWCHRT_2 BY WWCHRT_3              16.664     0.212      0.199        0.199
## WWCHRT_3 ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_3              16.665     1.020      1.020        1.020
## 
## WITH Statements
## 
## WCHRT_1  WITH WCHRT_B             16.379     0.000      0.000      999.000
## WCHRT_2  WITH WCHRT_B             21.686     0.000      0.000      999.000
## WCHRT_3  WITH WCHRT_B             13.418     0.000      0.000      999.000
## WWCHRT_B WITH RI_WCHRT            21.358    -0.001     -0.366       -0.366
## WWCHRT_1 WITH WWCHRT_B            12.868     0.000     -0.153       -0.153
## WWCHRT_2 WITH RI_WCHRT            17.274     0.000      0.119        0.119
## WWCHRT_2 WITH WWCHRT_B            18.626     0.000      0.284        0.284
## WWCHRT_3 WITH WWCHRT_B            10.618     0.000     -0.226       -0.226
## WWCHRT_3 WITH WWCHRT_1            13.024     0.000      0.192        0.192
## 
## Variances/Residual Variances
## 
## WCHRT_B                           12.868     0.001      0.001        0.204
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\wchr constrained.dgm
## 
##      Beginning Time:  12:39:37
##         Ending Time:  12:39:38
##        Elapsed Time:  00:00:01
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Loglikelihood test for Waist Circumference to Height Ratio

https://www.statmodel.com/chidiff.shtml

#install.packages("stats")
library(stats)

# Number of Free Parameters                       12
# Loglikelihood
#          H0 Value                       42900.924
#          H0 Scaling Correction Factor      8.5361
#            for MLR
#          H1 Value                       42910.217
#          H1 Scaling Correction Factor      7.7273
#            for MLR

# Unconstrained
L1 <- 42900.924  # Loglikelihood for the H1 model
c1 <- 8.5361  # Scaling correction factor for the H1 model
p1 <- 12     # Number of parameters for the H1 model

# Number of Free Parameters                       10
# Loglikelihood
#          H0 Value                       42844.638
#          H0 Scaling Correction Factor      9.5102
#            for MLR
#          H1 Value                       42910.217
#          H1 Scaling Correction Factor      7.7273
#            for MLR

# Constrained
L0 <- 42844.638  # Loglikelihood for the H0 model
c0 <- 9.5102  # Scaling correction factor for the H0 model
p0 <- 10    # Number of parameters for the H0 model

# Compute the difference test scaling correction (cd)
cd <- (p0 * c0 - p1 * c1) / (p0 - p1)

# Compute the chi-square difference test (TRd)
TRd <- -2 * (L0 - L1) / cd

# Define degrees of freedom
df <- p1 - p0

# Calculate p-value
p_value <- pchisq(TRd, df = df, lower.tail = FALSE)

# Print results
cat("Difference Test Scaling Correction (cd):", cd, "\n")

## Difference Test Scaling Correction (cd): 3.6656

cat("Chi-Square Difference Test (TRd):", TRd, "\n")

## Chi-Square Difference Test (TRd): 30.71039

cat("p-value:", p_value, "\n")

## p-value: 2.144489e-07

# Print "Cannot constrain" if p-value is less than 0.05
if (p_value < 0.05) {
  cat("Cannot constrain\n")
} else {
  cat("Constraining is acceptable\n")
}

## Cannot constrain

Puberty

Puberty Unconstrained model

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/puberty unconstrained.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024   1:02 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Puberty Unconstrained Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random pubtercept)
##   RI_pubt BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
## 
##   ! Create within-person centered variables
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Estimate the Lagged Effects
##   wpubt_1 ON wpubt_b;
##   wpubt_2 ON wpubt_1;
##   wpubt_3 ON wpubt_2;
## 
##   ! Constrain the measurement error variances to zero
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! ask for variances for all variables that are included;
##   [pubt_b pubt_1 pubt_2 pubt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_pubt with wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2299
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Puberty Unconstrained Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10157
## 
## Number of dependent variables                                    4
## Number of independent variables                                  0
## Number of continuous latent variables                            5
## 
## Observed dependent variables
## 
##   Continuous
##    PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_PUBT     WPUBT_B     WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns            15
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               PUBT_B        PUBT_1        PUBT_2        PUBT_3
##               ________      ________      ________      ________
##  PUBT_B         0.823
##  PUBT_1         0.375         0.416
##  PUBT_2         0.728         0.393         0.892
##  PUBT_3         0.691         0.387         0.800         0.846
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      PUBT_B                0.000       0.125      -1.606    0.08%      -0.935      0.035      0.053
##             8363.000       0.652      -0.580       3.081    0.01%       0.073      0.820
##      PUBT_1                0.000      -0.042      -2.124    0.05%      -0.843     -0.054      0.036
##             4224.000       0.636      -0.382       3.082    0.02%       0.157      0.790
##      PUBT_2                0.000      -0.276      -2.839    0.01%      -0.610     -0.151      0.041
##             9064.000       0.600       0.112       3.016    0.01%       0.232      0.660
##      PUBT_3                0.000      -0.457      -2.940    0.01%      -0.583     -0.036      0.115
##             8592.000       0.552       0.549       2.534    0.02%       0.252      0.554
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       12
## 
## Loglikelihood
## 
##           H0 Value                      -32956.741
##           H0 Scaling Correction Factor      1.0634
##             for MLR
##           H1 Value                      -32935.686
##           H1 Scaling Correction Factor      1.0532
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                   65937.483
##           Bayesian (BIC)                 66024.194
##           Sample-Size Adjusted BIC       65986.059
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                             42.454*
##           Degrees of Freedom                     2
##           P-Value                           0.0000
##           Scaling Correction Factor         0.9919
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.045
##           90 Percent C.I.                    0.034  0.057
##           Probability RMSEA <= .05           0.753
## 
## CFI/TLI
## 
##           CFI                                0.990
##           TLI                                0.970
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           4108.968
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.016
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_PUBT  BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  ON
##     WPUBT_B            0.250      0.022     11.203      0.000
## 
##  WPUBT_2  ON
##     WPUBT_1            0.369      0.020     18.464      0.000
## 
##  WPUBT_3  ON
##     WPUBT_2            0.385      0.016     24.451      0.000
## 
##  RI_PUBT  WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     PUBT_B             0.000      0.009      0.051      0.959
##     PUBT_1             0.029      0.011      2.604      0.009
##     PUBT_2             0.004      0.008      0.525      0.600
##     PUBT_3             0.003      0.008      0.399      0.690
## 
##  Variances
##     RI_PUBT            0.112      0.009     12.188      0.000
##     WPUBT_B            0.544      0.011     47.326      0.000
## 
##  Residual Variances
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WPUBT_1            0.482      0.012     38.830      0.000
##     WPUBT_2            0.416      0.008     49.789      0.000
##     WPUBT_3            0.369      0.008     47.181      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.277E-01
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_PUBT  BY
##     PUBT_B             0.413      0.017     24.726      0.000
##     PUBT_1             0.422      0.018     23.189      0.000
##     PUBT_2             0.433      0.018     24.164      0.000
##     PUBT_3             0.450      0.018     24.737      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.911      0.008    119.907      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.906      0.008    106.773      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.901      0.009    104.806      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.893      0.009     97.417      0.000
## 
##  WPUBT_1  ON
##     WPUBT_B            0.257      0.022     11.742      0.000
## 
##  WPUBT_2  ON
##     WPUBT_1            0.380      0.020     18.735      0.000
## 
##  WPUBT_3  ON
##     WPUBT_2            0.404      0.016     25.712      0.000
## 
##  RI_PUBT  WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     PUBT_B             0.001      0.011      0.051      0.959
##     PUBT_1             0.037      0.014      2.604      0.009
##     PUBT_2             0.005      0.010      0.524      0.600
##     PUBT_3             0.004      0.011      0.398      0.690
## 
##  Variances
##     RI_PUBT            1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WPUBT_1            0.934      0.011     83.207      0.000
##     WPUBT_2            0.855      0.015     55.399      0.000
##     WPUBT_3            0.836      0.013     65.731      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WPUBT_1            0.066      0.011      5.871      0.000
##     WPUBT_2            0.145      0.015      9.368      0.000
##     WPUBT_3            0.164      0.013     12.856      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_PUBT  BY PUBT_B                22.181    -0.672     -0.225       -0.278
## RI_PUBT  BY PUBT_1                10.205     0.259      0.087        0.109
## WPUBT_B  BY PUBT_2                10.875     0.038      0.028        0.037
## WPUBT_B  BY PUBT_3                28.350    -0.085     -0.062       -0.084
## WPUBT_1  BY PUBT_2                22.178    -0.225     -0.162       -0.209
## WPUBT_1  BY PUBT_3                22.182     0.087      0.062        0.084
## WPUBT_3  BY PUBT_B                42.339    -0.174     -0.116       -0.143
## WPUBT_3  BY PUBT_1                27.548     0.099      0.066        0.083
## WPUBT_3  BY PUBT_2                22.223    -0.265     -0.176       -0.227
## 
## ON/BY Statements
## 
## RI_PUBT  ON WPUBT_B  /
## WPUBT_B  BY RI_PUBT               22.166    -0.205     -0.452       -0.452
## RI_PUBT  ON WPUBT_1  /
## WPUBT_1  BY RI_PUBT               22.221     0.141      0.303        0.303
## WPUBT_B  ON RI_PUBT  /
## RI_PUBT  BY WPUBT_B               22.166    -0.996     -0.452       -0.452
## WPUBT_B  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_B               39.985    -0.220     -0.198       -0.198
## WPUBT_1  ON RI_PUBT  /
## RI_PUBT  BY WPUBT_1               22.213     0.518      0.241        0.241
## WPUBT_1  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_1               28.271     0.114      0.106        0.106
## WPUBT_2  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_2               22.234    -0.265     -0.252       -0.252
## WPUBT_3  ON WPUBT_B  /
## WPUBT_B  BY WPUBT_3               28.350    -0.085     -0.094       -0.094
## WPUBT_3  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_3               22.182     0.087      0.094        0.094
## 
## WITH Statements
## 
## PUBT_2   WITH PUBT_B              13.292     0.022      0.022      999.000
## PUBT_2   WITH PUBT_1              42.177    -0.110     -0.110      999.000
## PUBT_3   WITH PUBT_B              35.872    -0.045     -0.045      999.000
## PUBT_3   WITH PUBT_1              31.452     0.040      0.040      999.000
## PUBT_3   WITH PUBT_2              22.233    -0.098     -0.098      999.000
## WPUBT_B  WITH RI_PUBT             22.166    -0.112     -0.452       -0.452
## WPUBT_1  WITH RI_PUBT             22.213     0.058      0.250        0.250
## WPUBT_3  WITH WPUBT_B             28.350    -0.046     -0.103       -0.103
## WPUBT_3  WITH WPUBT_1             32.637     0.046      0.110        0.110
## WPUBT_3  WITH WPUBT_2             22.236    -0.098     -0.249       -0.249
## 
## Variances/Residual Variances
## 
## PUBT_2                            22.236     0.254      0.254        0.424
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\puberty unconstrained.dgm
## 
##      Beginning Time:  13:02:48
##         Ending Time:  13:02:49
##        Elapsed Time:  00:00:01
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Puberty Constrained model

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/puberty constrained.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024   1:06 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Puberty Unconstrained Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random pubtercept)
##   RI_pubt BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
## 
##   ! Create within-person centered variables
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Estimate the Lagged Effects
##   wpubt_1 ON wpubt_b (1);
##   wpubt_2 ON wpubt_1 (1);
##   wpubt_3 ON wpubt_2 (1);
## 
##   ! Constrain the measurement error variances to zero
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! ask for variances for all variables that are included;
##   [pubt_b pubt_1 pubt_2 pubt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_pubt with wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2299
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Puberty Unconstrained Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10157
## 
## Number of dependent variables                                    4
## Number of independent variables                                  0
## Number of continuous latent variables                            5
## 
## Observed dependent variables
## 
##   Continuous
##    PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_PUBT     WPUBT_B     WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns            15
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               PUBT_B        PUBT_1        PUBT_2        PUBT_3
##               ________      ________      ________      ________
##  PUBT_B         0.823
##  PUBT_1         0.375         0.416
##  PUBT_2         0.728         0.393         0.892
##  PUBT_3         0.691         0.387         0.800         0.846
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      PUBT_B                0.000       0.125      -1.606    0.08%      -0.935      0.035      0.053
##             8363.000       0.652      -0.580       3.081    0.01%       0.073      0.820
##      PUBT_1                0.000      -0.042      -2.124    0.05%      -0.843     -0.054      0.036
##             4224.000       0.636      -0.382       3.082    0.02%       0.157      0.790
##      PUBT_2                0.000      -0.276      -2.839    0.01%      -0.610     -0.151      0.041
##             9064.000       0.600       0.112       3.016    0.01%       0.232      0.660
##      PUBT_3                0.000      -0.457      -2.940    0.01%      -0.583     -0.036      0.115
##             8592.000       0.552       0.549       2.534    0.02%       0.252      0.554
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       10
## 
## Loglikelihood
## 
##           H0 Value                      -32982.169
##           H0 Scaling Correction Factor      1.0510
##             for MLR
##           H1 Value                      -32935.686
##           H1 Scaling Correction Factor      1.0532
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                   65984.337
##           Bayesian (BIC)                 66056.596
##           Sample-Size Adjusted BIC       66024.818
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                             87.813*
##           Degrees of Freedom                     4
##           P-Value                           0.0000
##           Scaling Correction Factor         1.0587
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.045
##           90 Percent C.I.                    0.037  0.054
##           Probability RMSEA <= .05           0.806
## 
## CFI/TLI
## 
##           CFI                                0.980
##           TLI                                0.969
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           4108.968
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.034
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_PUBT  BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  ON
##     WPUBT_B            0.357      0.016     22.619      0.000
## 
##  WPUBT_2  ON
##     WPUBT_1            0.357      0.016     22.619      0.000
## 
##  WPUBT_3  ON
##     WPUBT_2            0.357      0.016     22.619      0.000
## 
##  RI_PUBT  WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     PUBT_B             0.001      0.009      0.059      0.953
##     PUBT_1             0.030      0.011      2.670      0.008
##     PUBT_2             0.004      0.008      0.527      0.598
##     PUBT_3             0.003      0.008      0.376      0.707
## 
##  Variances
##     RI_PUBT            0.106      0.010     10.732      0.000
##     WPUBT_B            0.555      0.011     50.066      0.000
## 
##  Residual Variances
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WPUBT_1            0.495      0.013     38.361      0.000
##     WPUBT_2            0.418      0.009     48.866      0.000
##     WPUBT_3            0.368      0.008     45.369      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.516E-01
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_PUBT  BY
##     PUBT_B             0.401      0.018     22.266      0.000
##     PUBT_1             0.398      0.020     20.253      0.000
##     PUBT_2             0.423      0.020     21.005      0.000
##     PUBT_3             0.445      0.021     21.446      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.916      0.008    116.159      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.917      0.009    107.662      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.906      0.009     96.621      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.895      0.010     86.773      0.000
## 
##  WPUBT_1  ON
##     WPUBT_B            0.354      0.014     25.226      0.000
## 
##  WPUBT_2  ON
##     WPUBT_1            0.384      0.018     21.570      0.000
## 
##  WPUBT_3  ON
##     WPUBT_2            0.380      0.017     22.237      0.000
## 
##  RI_PUBT  WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     PUBT_B             0.001      0.011      0.059      0.953
##     PUBT_1             0.036      0.014      2.670      0.008
##     PUBT_2             0.005      0.010      0.527      0.598
##     PUBT_3             0.004      0.011      0.376      0.707
## 
##  Variances
##     RI_PUBT            1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WPUBT_1            0.875      0.010     88.322      0.000
##     WPUBT_2            0.853      0.014     62.505      0.000
##     WPUBT_3            0.855      0.013     65.686      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WPUBT_1            0.125      0.010     12.613      0.000
##     WPUBT_2            0.147      0.014     10.785      0.000
##     WPUBT_3            0.145      0.013     11.118      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_PUBT  BY PUBT_B                55.930    -0.886     -0.289       -0.355
## WPUBT_B  BY PUBT_B                45.671     0.348      0.259        0.318
## WPUBT_B  BY PUBT_1                47.686    -0.119     -0.089       -0.108
## WPUBT_B  BY PUBT_3                15.659    -0.068     -0.051       -0.069
## WPUBT_1  BY PUBT_B                45.675    -0.162     -0.122       -0.150
## WPUBT_1  BY PUBT_1                21.859    -0.137     -0.103       -0.125
## WPUBT_1  BY PUBT_3                41.122     0.103      0.078        0.106
## WPUBT_2  BY PUBT_3                17.884     0.062      0.043        0.059
## WPUBT_3  BY PUBT_B                60.923    -0.206     -0.135       -0.166
## WPUBT_3  BY PUBT_1                32.789     0.108      0.071        0.086
## WPUBT_3  BY PUBT_3                17.834     0.173      0.114        0.155
## 
## ON/BY Statements
## 
## RI_PUBT  ON WPUBT_B  /
## WPUBT_B  BY RI_PUBT               62.300    -0.192     -0.438       -0.438
## RI_PUBT  ON WPUBT_2  /
## WPUBT_2  BY RI_PUBT               12.008     0.079      0.170        0.170
## RI_PUBT  ON WPUBT_3  /
## WPUBT_3  BY RI_PUBT               17.836     0.083      0.167        0.167
## WPUBT_B  ON RI_PUBT  /
## RI_PUBT  BY WPUBT_B               62.300    -1.000     -0.438       -0.438
## WPUBT_B  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_B               45.680    -0.139     -0.140       -0.140
## WPUBT_B  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_B               44.654    -0.263     -0.232       -0.232
## WPUBT_1  ON WPUBT_B  /
## WPUBT_B  BY WPUBT_1               45.679    -0.098     -0.097       -0.097
## WPUBT_1  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_1               45.714    -0.348     -0.348       -0.348
## WPUBT_1  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_1               53.790     0.152      0.132        0.132
## WPUBT_2  ON RI_PUBT  /
## RI_PUBT  BY WPUBT_2               13.784     0.286      0.133        0.133
## WPUBT_3  ON WPUBT_B  /
## WPUBT_B  BY WPUBT_3               15.659    -0.068     -0.077       -0.077
## WPUBT_3  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_3               41.122     0.103      0.118        0.118
## WPUBT_3  ON WPUBT_2  /
## WPUBT_2  BY WPUBT_3               17.884     0.031      0.033        0.033
## WPUBT_3  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_3               17.834     0.173      0.173        0.173
## 
## WITH Statements
## 
## PUBT_1   WITH PUBT_B              50.010    -0.070     -0.070      999.000
## PUBT_3   WITH PUBT_B              35.220    -0.046     -0.046      999.000
## PUBT_3   WITH PUBT_1              38.303     0.045      0.045      999.000
## WPUBT_B  WITH RI_PUBT             62.300    -0.106     -0.438       -0.438
## WPUBT_1  WITH WPUBT_B             45.679    -0.069     -0.131       -0.131
## WPUBT_2  WITH RI_PUBT             13.784     0.030      0.144        0.144
## WPUBT_3  WITH WPUBT_B             15.659    -0.038     -0.084       -0.084
## WPUBT_3  WITH WPUBT_1             53.530     0.055      0.129        0.129
## 
## Variances/Residual Variances
## 
## PUBT_B                            45.672     0.193      0.193        0.292
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\puberty constrained.dgm
## 
##      Beginning Time:  13:06:18
##         Ending Time:  13:06:18
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Loglikelihood test for Puberty

https://www.statmodel.com/chidiff.shtml

#install.packages("stats")
library(stats)

# Number of Free Parameters                       12
# Loglikelihood
#          H0 Value                      -32956.741
#          H0 Scaling Correction Factor      1.0634
#            for MLR
#          H1 Value                      -32935.686
#          H1 Scaling Correction Factor      1.0532
#            for MLR

# Unconstrained
L1 <- -32956.741  # Loglikelihood for the H1 model
c1 <- 1.0634  # Scaling correction factor for the H1 model
p1 <- 12     # Number of parameters for the H1 model

# Number of Free Parameters                       10
# Loglikelihood
#          H0 Value                      -32982.169
#          H0 Scaling Correction Factor      1.0510
#            for MLR
#          H1 Value                      -32935.686
#          H1 Scaling Correction Factor      1.0532
#            for MLR

# Constrained
L0 <- -32982.169  # Loglikelihood for the H0 model
c0 <-  1.0510  # Scaling correction factor for the H0 model
p0 <- 10    # Number of parameters for the H0 model

# Compute the difference test scaling correction (cd)
cd <- (p0 * c0 - p1 * c1) / (p0 - p1)

# Compute the chi-square difference test (TRd)
TRd <- -2 * (L0 - L1) / cd

# Define degrees of freedom
df <- p1 - p0

# Calculate p-value
p_value <- pchisq(TRd, df = df, lower.tail = FALSE)

# Print results
cat("Difference Test Scaling Correction (cd):", cd, "\n")

## Difference Test Scaling Correction (cd): 1.1254

cat("Chi-Square Difference Test (TRd):", TRd, "\n")

## Chi-Square Difference Test (TRd): 45.18927

cat("p-value:", p_value, "\n")

## p-value: 1.539131e-10

# Print "Cannot constrain" if p-value is less than 0.05
if (p_value < 0.05) {
  cat("Cannot constrain\n")
} else {
  cat("Constraining is acceptable\n")
}

## Cannot constrain

Summary: Based on the above model building steps of estimating models with unconstrained and constrained cross lagged paths and then performing likelihood ratio tests to rest if constraining results in decrements in model fit, all cross lagged paths should be left unconstrained.

Full Sample Model

Full random intercept cross lag panel model specified according to Hamaker et al.,2015 (DOI: 10.1037/a0038889)

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/all full model.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024   2:02 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Full Sample Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3
##   intt_b intt_1
##   intt_2 intt_3
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   DEFINE:
##   wchrt_b = wchrt_b*10;
##   wchrt_1 = wchrt_1*10;
##   wchrt_2 = wchrt_2*10;
##   wchrt_3 = wchrt_3*10;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
##   RI_pubtT BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! RI correlations
##   RI_intt with RI_pubtT RI_wchrt;
##   RI_pubtT with RI_wchrt;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b;
##   wwchrt_1 ON wintt_b;
##   wwchrt_1 ON wpubt_b;
## 
##   wwchrt_2 ON wwchrt_1;
##   wwchrt_2 ON wintt_1;
##   wwchrt_2 ON wpubt_1;
## 
##   wwchrt_3 ON wwchrt_2;
##   wwchrt_3 ON wintt_2;
##   wwchrt_3 ON wpubt_2;
## 
##   wpubt_1 ON wpubt_b;
##   wpubt_1 ON wintt_b;
##   wpubt_1 ON wwchrt_b;
## 
##   wpubt_2 ON wpubt_1;
##   wpubt_2 ON wintt_1;
##   wpubt_2 ON wwchrt_1;
## 
##   wpubt_3 ON wpubt_2;
##   wpubt_3 ON wintt_2;
##   wpubt_3 ON wwchrt_2;
## 
##   wintt_1 ON wintt_b;
##   wintt_1 ON wpubt_b;
##   wintt_1 ON wwchrt_b;
## 
##   wintt_2 ON wintt_1;
##   wintt_2 ON wpubt_1;
##   wintt_2 ON wwchrt_1;
## 
##   wintt_3 ON wintt_2;
##   wintt_3 ON wpubt_2;
##   wintt_3 ON wwchrt_2;
## 
##   ! Estimate the covariance between the within-person
##   ! centered variables at the first wave
##   wintt_b with wpubt_b;
##   wwchrt_b with wintt_b wpubt_b;
## 
##   ! Estimate covariances between residuals of within-person components
##   ! (i.e., innovations)
##   wintt_1 with wpubt_1 wwchrt_1;
##   wpubt_1 with wwchrt_1;
## 
##   wintt_2 with wpubt_2 wwchrt_2;
##   wpubt_2 with wwchrt_2;
## 
##   wintt_3 with wpubt_3 wwchrt_3;
##   wpubt_3 with wwchrt_3;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
##   [pubt_b pubt_1 pubt_2 pubt_3];
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_intt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_pubtT with wwchrt_b@0 wintt_b@0 wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES Tech4;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2094
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Full Sample Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                       10362
## 
## Number of dependent variables                                   12
## Number of independent variables                                  0
## Number of continuous latent variables                           15
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3     INTT_B      INTT_1
##    INTT_2      INTT_3      PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_INTT     RI_PUBTT    RI_WCHRT    WINTT_B     WINTT_1     WINTT_2
##    WINTT_3     WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3    WPUBT_B
##    WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns           208
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3       INTT_B
##               ________      ________      ________      ________      ________
##  WCHRT_B        0.998
##  WCHRT_1        0.936         0.937
##  WCHRT_2        0.763         0.746         0.764
##  WCHRT_3        0.169         0.166         0.153         0.169
##  INTT_B         0.998         0.937         0.764         0.169         0.999
##  INTT_1         0.942         0.936         0.749         0.167         0.943
##  INTT_2         0.917         0.891         0.763         0.167         0.918
##  INTT_3         0.850         0.827         0.709         0.168         0.851
##  PUBT_B         0.806         0.757         0.626         0.149         0.807
##  PUBT_1         0.407         0.405         0.392         0.102         0.407
##  PUBT_2         0.873         0.849         0.727         0.158         0.874
##  PUBT_3         0.828         0.805         0.691         0.162         0.829
## 
## 
##            Covariance Coverage
##               INTT_1        INTT_2        INTT_3        PUBT_B        PUBT_1
##               ________      ________      ________      ________      ________
##  INTT_1         0.944
##  INTT_2         0.897         0.919
##  INTT_3         0.833         0.833         0.851
##  PUBT_B         0.762         0.743         0.690         0.807
##  PUBT_1         0.407         0.398         0.384         0.368         0.408
##  PUBT_2         0.854         0.869         0.794         0.714         0.385
##  PUBT_3         0.810         0.810         0.812         0.677         0.379
## 
## 
##            Covariance Coverage
##               PUBT_2        PUBT_3
##               ________      ________
##  PUBT_2         0.875
##  PUBT_3         0.784         0.829
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B               0.000       1.308      -2.415    0.01%      -0.550     -0.290     -0.144
##            10342.000       0.487       4.917       8.909    0.01%       0.018      0.508
##      WCHRT_1               0.000       2.054      -2.125    0.01%      -0.582     -0.308     -0.165
##             9711.000       0.566      13.985       9.968    0.01%       0.007      0.536
##      WCHRT_2               0.000       1.516      -2.197    0.01%      -0.622     -0.327     -0.174
##             7917.000       0.597       6.773       9.219    0.01%       0.019      0.563
##      WCHRT_3               0.000       1.723      -1.493    0.06%      -0.681     -0.376     -0.222
##             1754.000       0.720       7.313       7.699    0.06%      -0.010      0.635
##      INTT_B                0.000       2.512      -1.161    0.27%      -1.096     -0.934     -0.912
##            10355.000       2.893       8.153      13.915    0.01%      -0.129      0.904
##      INTT_1                0.000       2.416      -1.298    0.01%      -1.130     -1.052     -0.986
##             9780.000       3.147       7.265      12.912    0.01%      -0.139      0.905
##      INTT_2                0.000       2.363      -1.697    0.01%      -1.274     -1.119     -1.024
##             9519.000       3.840       7.067      15.034    0.01%      -0.293      0.867
##      INTT_3                0.000       2.123      -1.822    0.02%      -1.459     -1.307     -0.672
##             8819.000       4.614       5.379      13.693    0.01%      -0.398      1.370
##      PUBT_B                0.000       0.125      -1.606    0.08%      -0.935      0.035      0.053
##             8363.000       0.652      -0.580       3.081    0.01%       0.073      0.820
##      PUBT_1                0.000      -0.042      -2.124    0.05%      -0.843     -0.054      0.036
##             4224.000       0.636      -0.382       3.082    0.02%       0.157      0.790
##      PUBT_2                0.000      -0.276      -2.839    0.01%      -0.610     -0.151      0.041
##             9064.000       0.600       0.112       3.016    0.01%       0.232      0.660
##      PUBT_3                0.000      -0.457      -2.940    0.01%      -0.583     -0.036      0.115
##             8592.000       0.552       0.549       2.534    0.02%       0.252      0.554
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       69
## 
## Loglikelihood
## 
##           H0 Value                     -129524.375
##           H0 Scaling Correction Factor      2.6656
##             for MLR
##           H1 Value                     -129439.944
##           H1 Scaling Correction Factor      2.3436
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  259186.750
##           Bayesian (BIC)                259686.717
##           Sample-Size Adjusted BIC      259467.444
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                            131.349*
##           Degrees of Freedom                    21
##           P-Value                           0.0000
##           Scaling Correction Factor         1.2856
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.023
##           90 Percent C.I.                    0.019  0.026
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.993
##           TLI                                0.977
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                          15223.002
##           Degrees of Freedom                    66
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.012
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  RI_PUBTT BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.118      0.072     -1.643      0.100
##     WINTT_B           -0.023      0.012     -1.919      0.055
##     WPUBT_B            0.005      0.013      0.359      0.719
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.203      0.038      5.278      0.000
##     WINTT_1            0.019      0.010      1.922      0.055
##     WPUBT_1            0.014      0.018      0.794      0.427
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.493      0.077      6.363      0.000
##     WINTT_2            0.000      0.010      0.044      0.965
##     WPUBT_2           -0.031      0.021     -1.509      0.131
## 
##  WPUBT_1  ON
##     WPUBT_B            0.252      0.023     11.204      0.000
##     WINTT_B           -0.001      0.019     -0.064      0.949
##     WWCHRT_B          -0.018      0.092     -0.195      0.845
## 
##  WPUBT_2  ON
##     WPUBT_1            0.368      0.020     18.189      0.000
##     WINTT_1           -0.001      0.010     -0.058      0.953
##     WWCHRT_1          -0.048      0.022     -2.236      0.025
## 
##  WPUBT_3  ON
##     WPUBT_2            0.386      0.016     24.272      0.000
##     WINTT_2            0.009      0.006      1.554      0.120
##     WWCHRT_2          -0.028      0.018     -1.516      0.129
## 
##  WINTT_1  ON
##     WINTT_B            0.056      0.047      1.177      0.239
##     WPUBT_B            0.015      0.030      0.493      0.622
##     WWCHRT_B           0.099      0.129      0.763      0.445
## 
##  WINTT_2  ON
##     WINTT_1            0.232      0.036      6.368      0.000
##     WPUBT_1            0.094      0.043      2.178      0.029
##     WWCHRT_1          -0.040      0.046     -0.875      0.382
## 
##  WINTT_3  ON
##     WINTT_2            0.425      0.025     16.708      0.000
##     WPUBT_2            0.092      0.030      3.018      0.003
##     WWCHRT_2           0.133      0.054      2.448      0.014
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.040      0.013      3.050      0.002
##     RI_WCHRT           0.128      0.014      9.100      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.071      0.005     13.510      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B            0.011      0.015      0.753      0.451
##     WWCHRT_B          -0.017      0.010     -1.705      0.088
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B           -0.005      0.006     -0.935      0.350
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1            0.003      0.021      0.139      0.889
##     WWCHRT_1           0.006      0.015      0.374      0.708
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.001      0.010      0.085      0.932
## 
##  WINTT_2  WITH
##     WPUBT_2            0.018      0.012      1.454      0.146
##     WWCHRT_2           0.017      0.010      1.655      0.098
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.011      0.004     -2.579      0.010
## 
##  WINTT_3  WITH
##     WPUBT_3            0.043      0.011      3.869      0.000
##     WWCHRT_3           0.030      0.022      1.378      0.168
## 
##  WPUBT_3  WITH
##     WWCHRT_3          -0.003      0.008     -0.350      0.727
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.007      0.042      0.967
##     WCHRT_1            0.006      0.008      0.741      0.459
##     WCHRT_2            0.016      0.008      1.979      0.048
##     WCHRT_3           -0.070      0.014     -5.128      0.000
##     INTT_B             0.001      0.017      0.041      0.967
##     INTT_1             0.009      0.018      0.507      0.612
##     INTT_2             0.011      0.020      0.532      0.595
##     INTT_3             0.026      0.023      1.144      0.252
##     PUBT_B             0.002      0.009      0.210      0.833
##     PUBT_1             0.033      0.011      2.964      0.003
##     PUBT_2             0.006      0.008      0.711      0.477
##     PUBT_3             0.005      0.008      0.660      0.509
## 
##  Variances
##     RI_INTT            1.846      0.070     26.308      0.000
##     RI_PUBTT           0.111      0.009     12.019      0.000
##     RI_WCHRT           0.388      0.010     40.198      0.000
##     WINTT_B            1.112      0.066     16.745      0.000
##     WWCHRT_B           0.101      0.012      8.705      0.000
##     WPUBT_B            0.545      0.012     47.249      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.233      0.074     16.639      0.000
##     WINTT_2            1.956      0.076     25.616      0.000
##     WINTT_3            2.456      0.079     31.028      0.000
##     WWCHRT_1           0.174      0.023      7.492      0.000
##     WWCHRT_2           0.216      0.017     12.566      0.000
##     WWCHRT_3           0.243      0.037      6.496      0.000
##     WPUBT_1            0.483      0.013     38.455      0.000
##     WPUBT_2            0.414      0.008     49.764      0.000
##     WPUBT_3            0.371      0.008     47.376      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.437E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.790      0.011     72.908      0.000
##     INTT_1             0.774      0.013     60.440      0.000
##     INTT_2             0.690      0.010     67.821      0.000
##     INTT_3             0.628      0.010     63.556      0.000
## 
##  RI_PUBTT BY
##     PUBT_B             0.412      0.017     24.370      0.000
##     PUBT_1             0.421      0.018     22.833      0.000
##     PUBT_2             0.432      0.018     23.838      0.000
##     PUBT_3             0.448      0.018     24.375      0.000
## 
##  RI_WCHRT BY
##     WCHRT_B            0.891      0.011     78.513      0.000
##     WCHRT_1            0.829      0.018     47.219      0.000
##     WCHRT_2            0.796      0.012     65.715      0.000
##     WCHRT_3            0.752      0.025     30.629      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.613      0.014     43.908      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.633      0.016     40.509      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.724      0.010     74.509      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.778      0.008     97.607      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.454      0.022     20.347      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.559      0.026     21.452      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.605      0.016     37.922      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.659      0.028     23.523      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.911      0.008    119.346      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.907      0.009    106.241      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.902      0.009    103.828      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.894      0.009     97.229      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.089      0.054     -1.651      0.099
##     WINTT_B           -0.057      0.030     -1.906      0.057
##     WPUBT_B            0.008      0.023      0.358      0.720
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.180      0.032      5.611      0.000
##     WINTT_1            0.045      0.024      1.870      0.062
##     WPUBT_1            0.022      0.027      0.790      0.430
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.427      0.060      7.139      0.000
##     WINTT_2            0.001      0.025      0.044      0.965
##     WPUBT_2           -0.040      0.026     -1.507      0.132
## 
##  WPUBT_1  ON
##     WPUBT_B            0.259      0.022     11.761      0.000
##     WINTT_B           -0.002      0.028     -0.064      0.949
##     WWCHRT_B          -0.008      0.041     -0.195      0.845
## 
##  WPUBT_2  ON
##     WPUBT_1            0.380      0.021     18.377      0.000
##     WINTT_1           -0.001      0.016     -0.058      0.953
##     WWCHRT_1          -0.029      0.013     -2.270      0.023
## 
##  WPUBT_3  ON
##     WPUBT_2            0.404      0.016     25.515      0.000
##     WINTT_2            0.020      0.013      1.552      0.121
##     WWCHRT_2          -0.020      0.013     -1.528      0.127
## 
##  WINTT_1  ON
##     WINTT_B            0.053      0.044      1.186      0.236
##     WPUBT_B            0.010      0.020      0.493      0.622
##     WWCHRT_B           0.028      0.037      0.766      0.443
## 
##  WINTT_2  ON
##     WINTT_1            0.181      0.030      6.063      0.000
##     WPUBT_1            0.048      0.022      2.172      0.030
##     WWCHRT_1          -0.012      0.014     -0.873      0.383
## 
##  WINTT_3  ON
##     WINTT_2            0.359      0.020     17.544      0.000
##     WPUBT_2            0.038      0.013      3.030      0.002
##     WWCHRT_2           0.037      0.015      2.493      0.013
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.088      0.029      3.071      0.002
##     RI_WCHRT           0.152      0.016      9.599      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.344      0.028     12.263      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B            0.014      0.019      0.753      0.451
##     WWCHRT_B          -0.051      0.031     -1.672      0.095
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B           -0.023      0.025     -0.929      0.353
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1            0.004      0.027      0.139      0.889
##     WWCHRT_1           0.012      0.033      0.375      0.708
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.003      0.036      0.085      0.932
## 
##  WINTT_2  WITH
##     WPUBT_2            0.019      0.013      1.460      0.144
##     WWCHRT_2           0.025      0.016      1.633      0.103
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.036      0.014     -2.646      0.008
## 
##  WINTT_3  WITH
##     WPUBT_3            0.046      0.012      3.888      0.000
##     WWCHRT_3           0.039      0.029      1.341      0.180
## 
##  WPUBT_3  WITH
##     WWCHRT_3          -0.009      0.025     -0.348      0.728
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.010      0.042      0.967
##     WCHRT_1            0.007      0.010      0.746      0.456
##     WCHRT_2            0.021      0.010      2.010      0.044
##     WCHRT_3           -0.084      0.018     -4.737      0.000
##     INTT_B             0.000      0.010      0.041      0.967
##     INTT_1             0.005      0.010      0.510      0.610
##     INTT_2             0.005      0.010      0.535      0.592
##     INTT_3             0.012      0.010      1.158      0.247
##     PUBT_B             0.002      0.011      0.210      0.833
##     PUBT_1             0.042      0.014      2.964      0.003
##     PUBT_2             0.007      0.010      0.710      0.478
##     PUBT_3             0.007      0.011      0.659      0.510
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     RI_PUBTT           1.000      0.000    999.000    999.000
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.996      0.005    185.214      0.000
##     WINTT_2            0.965      0.011     86.719      0.000
##     WINTT_3            0.866      0.015     57.831      0.000
##     WWCHRT_1           0.989      0.010     96.054      0.000
##     WWCHRT_2           0.965      0.012     80.925      0.000
##     WWCHRT_3           0.815      0.051     16.046      0.000
##     WPUBT_1            0.933      0.011     82.894      0.000
##     WPUBT_2            0.855      0.016     54.703      0.000
##     WPUBT_3            0.835      0.013     65.507      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.004      0.005      0.651      0.515
##     WINTT_2            0.035      0.011      3.175      0.002
##     WINTT_3            0.134      0.015      8.926      0.000
##     WWCHRT_1           0.011      0.010      1.045      0.296
##     WWCHRT_2           0.035      0.012      2.930      0.003
##     WWCHRT_3           0.185      0.051      3.647      0.000
##     WPUBT_1            0.067      0.011      5.957      0.000
##     WPUBT_2            0.145      0.016      9.304      0.000
##     WPUBT_3            0.165      0.013     12.912      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_INTT  BY INTT_B                55.894    -0.229     -0.311       -0.181
## RI_INTT  BY INTT_1                49.855     0.175      0.237        0.135
## WINTT_B  BY INTT_3                41.521    -0.171     -0.180       -0.083
## WINTT_1  BY INTT_2                57.910    -0.438     -0.487       -0.248
## WINTT_1  BY INTT_3                58.958     0.188      0.209        0.097
## WINTT_3  BY INTT_B                53.905    -0.094     -0.158       -0.092
## WINTT_3  BY INTT_1                59.062     0.088      0.149        0.085
## WINTT_3  BY INTT_2                58.713    -0.638     -1.073       -0.545
## WWCHRT_B BY WCHRT_3               13.586    -0.247     -0.078       -0.094
## WWCHRT_1 BY WCHRT_2               13.890    -0.294     -0.123       -0.158
## WWCHRT_1 BY WCHRT_3               12.445     0.140      0.059        0.071
## WWCHRT_3 BY WCHRT_B               16.111    -0.132     -0.072       -0.103
## WWCHRT_3 BY WCHRT_1               12.424     0.103      0.056        0.075
## WWCHRT_3 BY WCHRT_2               13.810    -0.625     -0.341       -0.436
## WPUBT_B  BY PUBT_3                20.208    -0.081     -0.060       -0.080
## WPUBT_1  BY PUBT_2                19.088    -0.234     -0.169       -0.218
## WPUBT_1  BY PUBT_3                18.620     0.090      0.065        0.087
## WPUBT_3  BY PUBT_B                29.114    -0.162     -0.108       -0.133
## WPUBT_3  BY PUBT_1                23.033     0.102      0.068        0.086
## WPUBT_3  BY PUBT_2                20.345    -0.284     -0.189       -0.245
## 
## ON/BY Statements
## 
## RI_INTT  ON WINTT_B  /
## WINTT_B  BY RI_INTT               57.730    -0.407     -0.316       -0.316
## RI_INTT  ON WINTT_1  /
## WINTT_1  BY RI_INTT               59.475     0.327      0.268        0.268
## RI_PUBTT ON WPUBT_B  /
## WPUBT_B  BY RI_PUBTT              18.555    -0.213     -0.471       -0.471
## RI_PUBTT ON WPUBT_1  /
## WPUBT_1  BY RI_PUBTT              18.068     0.144      0.311        0.311
## RI_WCHRT ON WWCHRT_B /
## WWCHRT_B BY RI_WCHRT              11.605    -0.478     -0.244       -0.244
## RI_WCHRT ON WWCHRT_1 /
## WWCHRT_1 BY RI_WCHRT              10.154     0.245      0.165        0.165
## WINTT_B  ON RI_INTT  /
## RI_INTT  BY WINTT_B               55.625    -0.242     -0.312       -0.312
## WINTT_B  ON WINTT_3  /
## WINTT_3  BY WINTT_B               52.051    -0.097     -0.154       -0.154
## WINTT_1  ON RI_INTT  /
## RI_INTT  BY WINTT_1               58.395     0.212      0.259        0.259
## WINTT_1  ON WINTT_3  /
## WINTT_3  BY WINTT_1               58.921     0.091      0.138        0.138
## WINTT_2  ON WINTT_3  /
## WINTT_3  BY WINTT_2               58.714    -0.638     -0.754       -0.754
## WINTT_3  ON WINTT_B  /
## WINTT_B  BY WINTT_3               41.521    -0.171     -0.107       -0.107
## WINTT_3  ON WINTT_1  /
## WINTT_1  BY WINTT_3               58.958     0.188      0.124        0.124
## WWCHRT_B ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_B              15.988    -0.119     -0.204       -0.204
## WWCHRT_1 ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_1              12.377     0.106      0.138        0.138
## WWCHRT_2 ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_2              13.808    -0.625     -0.721       -0.721
## WWCHRT_3 ON WWCHRT_B /
## WWCHRT_B BY WWCHRT_3              13.586    -0.247     -0.143       -0.143
## WWCHRT_3 ON WWCHRT_1 /
## WWCHRT_1 BY WWCHRT_3              12.445     0.140      0.108        0.108
## WPUBT_B  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_B               25.762    -0.197     -0.178       -0.178
## WPUBT_1  ON RI_PUBTT /
## RI_PUBTT BY WPUBT_1               17.481     0.482      0.224        0.224
## WPUBT_1  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_1               23.511     0.118      0.109        0.109
## WPUBT_2  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_2               20.344    -0.284     -0.272       -0.272
## WPUBT_3  ON WPUBT_B  /
## WPUBT_B  BY WPUBT_3               20.208    -0.081     -0.090       -0.090
## WPUBT_3  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_3               18.620     0.090      0.097        0.097
## 
## WITH Statements
## 
## WCHRT_2  WITH WCHRT_1             11.140    -0.046     -0.046      999.000
## WCHRT_3  WITH WCHRT_B             12.988    -0.026     -0.026      999.000
## WCHRT_3  WITH WCHRT_1             11.803     0.024      0.024      999.000
## WCHRT_3  WITH WCHRT_2             12.338    -0.144     -0.144      999.000
## INTT_2   WITH INTT_1              60.519    -0.525     -0.525      999.000
## INTT_3   WITH INTT_B              44.253    -0.190     -0.190      999.000
## INTT_3   WITH INTT_1              60.002     0.219      0.219      999.000
## INTT_3   WITH INTT_2              58.841    -1.566     -1.566      999.000
## PUBT_2   WITH PUBT_1              33.347    -0.110     -0.110      999.000
## PUBT_3   WITH PUBT_B              26.156    -0.044     -0.044      999.000
## PUBT_3   WITH PUBT_1              25.905     0.041      0.041      999.000
## PUBT_3   WITH PUBT_2              19.963    -0.105     -0.105      999.000
## WINTT_B  WITH RI_INTT             59.046    -0.459     -0.320       -0.320
## WINTT_1  WITH RI_INTT             59.244     0.387      0.256        0.256
## WINTT_3  WITH WINTT_B             41.839    -0.191     -0.116       -0.116
## WINTT_3  WITH WINTT_1             59.887     0.227      0.130        0.130
## WINTT_3  WITH WINTT_2             58.840    -1.566     -0.714       -0.714
## WWCHRT_B WITH RI_WCHRT            11.423    -0.049     -0.247       -0.247
## WWCHRT_1 WITH RI_WCHRT            10.954     0.047      0.181        0.181
## WWCHRT_3 WITH WWCHRT_B            13.564    -0.025     -0.159       -0.159
## WWCHRT_3 WITH WWCHRT_1            11.776     0.025      0.122        0.122
## WWCHRT_3 WITH WWCHRT_2            12.338    -0.144     -0.628       -0.628
## WPUBT_B  WITH RI_PUBTT            17.989    -0.114     -0.464       -0.464
## WPUBT_1  WITH RI_PUBTT            18.371     0.060      0.258        0.258
## WPUBT_3  WITH WPUBT_B             20.159    -0.044     -0.098       -0.098
## WPUBT_3  WITH WPUBT_1             26.807     0.048      0.113        0.113
## WPUBT_3  WITH WPUBT_2             19.961    -0.105     -0.267       -0.267
## 
## Variances/Residual Variances
## 
## WCHRT_2                           15.782     0.323      0.323        0.528
## INTT_2                            58.572     3.680      3.680        0.950
## PUBT_2                            20.475     0.272      0.272        0.456
## 
## 
## TECHNICAL 4 OUTPUT
## 
## 
##      ESTIMATES DERIVED FROM THE MODEL
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.846
##  RI_PUBTT       0.040         0.111
##  RI_WCHRT       0.128         0.071         0.388
##  WINTT_B        0.000         0.000         0.000         1.112
##  WINTT_1        0.000         0.000         0.000         0.060         1.237
##  WINTT_2        0.000         0.000         0.000         0.015         0.287
##  WINTT_3        0.000         0.000         0.000         0.006         0.125
##  WWCHRT_B       0.000         0.000         0.000        -0.017         0.009
##  WWCHRT_1       0.000         0.000         0.000        -0.023         0.003
##  WWCHRT_2       0.000         0.000         0.000        -0.004         0.024
##  WWCHRT_3       0.000         0.000         0.000        -0.002         0.012
##  WPUBT_B        0.000         0.000         0.000         0.011         0.008
##  WPUBT_1        0.000         0.000         0.000         0.002         0.005
##  WPUBT_2        0.000         0.000         0.000         0.002         0.001
##  WPUBT_3        0.000         0.000         0.000         0.001         0.002
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        2.028
##  WINTT_3        0.868         2.835
##  WWCHRT_B       0.002         0.001         0.101
##  WWCHRT_1      -0.006         0.001        -0.011         0.176
##  WWCHRT_2       0.021         0.038        -0.002         0.036         0.224
##  WWCHRT_3       0.010         0.047        -0.001         0.018         0.111
##  WPUBT_B        0.015         0.011        -0.005         0.003         0.003
##  WPUBT_1        0.050         0.040        -0.003         0.002         0.008
##  WPUBT_2        0.036         0.059        -0.001        -0.008        -0.010
##  WPUBT_3        0.032         0.073         0.000        -0.004        -0.010
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.298
##  WPUBT_B        0.000         0.545
##  WPUBT_1       -0.002         0.137         0.518
##  WPUBT_2       -0.020         0.050         0.190         0.485
##  WPUBT_3       -0.013         0.020         0.074         0.188         0.444
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.070
##  RI_PUBTT       0.013         0.009
##  RI_WCHRT       0.014         0.005         0.010
##  WINTT_B        0.000         0.000         0.000         0.066
##  WINTT_1        0.000         0.000         0.000         0.054         0.079
##  WINTT_2        0.000         0.000         0.000         0.014         0.057
##  WINTT_3        0.000         0.000         0.000         0.006         0.028
##  WWCHRT_B       0.000         0.000         0.000         0.010         0.013
##  WWCHRT_1       0.000         0.000         0.000         0.012         0.014
##  WWCHRT_2       0.000         0.000         0.000         0.003         0.014
##  WWCHRT_3       0.000         0.000         0.000         0.002         0.008
##  WPUBT_B        0.000         0.000         0.000         0.015         0.017
##  WPUBT_1        0.000         0.000         0.000         0.023         0.023
##  WPUBT_2        0.000         0.000         0.000         0.009         0.016
##  WPUBT_3        0.000         0.000         0.000         0.003         0.007
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.087
##  WINTT_3        0.070         0.105
##  WWCHRT_B       0.003         0.002         0.012
##  WWCHRT_1       0.010         0.005         0.007         0.023
##  WWCHRT_2       0.012         0.014         0.001         0.007         0.018
##  WWCHRT_3       0.021         0.025         0.001         0.005         0.020
##  WPUBT_B        0.008         0.005         0.006         0.007         0.003
##  WPUBT_1        0.026         0.014         0.010         0.010         0.011
##  WPUBT_2        0.016         0.018         0.004         0.005         0.006
##  WPUBT_3        0.015         0.016         0.001         0.002         0.005
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.044
##  WPUBT_B        0.002         0.012
##  WPUBT_1        0.007         0.014         0.016
##  WPUBT_2        0.011         0.007         0.014         0.013
##  WPUBT_3        0.009         0.003         0.008         0.011         0.012
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT       26.308
##  RI_PUBTT       3.050        12.019
##  RI_WCHRT       9.100        13.510        40.198
##  WINTT_B        0.000         0.000         0.000        16.745
##  WINTT_1        0.000         0.000         0.000         1.111        15.675
##  WINTT_2        0.000         0.000         0.000         1.097         5.061
##  WINTT_3        0.000         0.000         0.000         0.977         4.489
##  WWCHRT_B       0.000         0.000         0.000        -1.705         0.675
##  WWCHRT_1       0.000         0.000         0.000        -1.935         0.232
##  WWCHRT_2       0.000         0.000         0.000        -1.118         1.679
##  WWCHRT_3       0.000         0.000         0.000        -1.110         1.528
##  WPUBT_B        0.000         0.000         0.000         0.753         0.484
##  WPUBT_1        0.000         0.000         0.000         0.077         0.200
##  WPUBT_2        0.000         0.000         0.000         0.204         0.053
##  WPUBT_3        0.000         0.000         0.000         0.273         0.350
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2       23.432
##  WINTT_3       12.336        26.984
##  WWCHRT_B       0.677         0.378         8.705
##  WWCHRT_1      -0.632         0.283        -1.759         7.796
##  WWCHRT_2       1.795         2.727        -1.659         4.958        12.766
##  WWCHRT_3       0.502         1.866        -1.624         3.580         5.531
##  WPUBT_B        1.746         2.490        -0.935         0.442         0.826
##  WPUBT_1        1.926         2.821        -0.317         0.180         0.720
##  WPUBT_2        2.223         3.179        -0.167        -1.484        -1.582
##  WPUBT_3        2.183         4.671        -0.108        -1.821        -1.934
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       6.788
##  WPUBT_B       -0.109        47.249
##  WPUBT_1       -0.282         9.916        32.237
##  WPUBT_2       -1.841         7.353        13.525        38.391
##  WPUBT_3       -1.468         6.171         9.795        17.103        36.710
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.002         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.266         0.000
##  WINTT_2        1.000         1.000         1.000         0.272         0.000
##  WINTT_3        1.000         1.000         1.000         0.329         0.000
##  WWCHRT_B       1.000         1.000         1.000         0.088         0.500
##  WWCHRT_1       1.000         1.000         1.000         0.053         0.816
##  WWCHRT_2       1.000         1.000         1.000         0.264         0.093
##  WWCHRT_3       1.000         1.000         1.000         0.267         0.127
##  WPUBT_B        1.000         1.000         1.000         0.451         0.629
##  WPUBT_1        1.000         1.000         1.000         0.938         0.841
##  WPUBT_2        1.000         1.000         1.000         0.839         0.958
##  WPUBT_3        1.000         1.000         1.000         0.785         0.727
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.499         0.706         0.000
##  WWCHRT_1       0.527         0.777         0.079         0.000
##  WWCHRT_2       0.073         0.006         0.097         0.000         0.000
##  WWCHRT_3       0.616         0.062         0.104         0.000         0.000
##  WPUBT_B        0.081         0.013         0.350         0.659         0.409
##  WPUBT_1        0.054         0.005         0.751         0.857         0.471
##  WPUBT_2        0.026         0.001         0.867         0.138         0.114
##  WPUBT_3        0.029         0.000         0.914         0.069         0.053
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.913         0.000
##  WPUBT_1        0.778         0.000         0.000
##  WPUBT_2        0.066         0.000         0.000         0.000
##  WPUBT_3        0.142         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.000
##  RI_PUBTT       0.088         1.000
##  RI_WCHRT       0.152         0.344         1.000
##  WINTT_B        0.000         0.000         0.000         1.000
##  WINTT_1        0.000         0.000         0.000         0.051         1.000
##  WINTT_2        0.000         0.000         0.000         0.010         0.181
##  WINTT_3        0.000         0.000         0.000         0.003         0.067
##  WWCHRT_B       0.000         0.000         0.000        -0.051         0.025
##  WWCHRT_1       0.000         0.000         0.000        -0.053         0.007
##  WWCHRT_2       0.000         0.000         0.000        -0.007         0.046
##  WWCHRT_3       0.000         0.000         0.000        -0.003         0.020
##  WPUBT_B        0.000         0.000         0.000         0.014         0.010
##  WPUBT_1        0.000         0.000         0.000         0.002         0.006
##  WPUBT_2        0.000         0.000         0.000         0.002         0.001
##  WPUBT_3        0.000         0.000         0.000         0.001         0.003
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.000
##  WINTT_3        0.362         1.000
##  WWCHRT_B       0.005         0.001         1.000
##  WWCHRT_1      -0.010         0.002        -0.086         1.000
##  WWCHRT_2       0.032         0.048        -0.015         0.180         1.000
##  WWCHRT_3       0.013         0.051        -0.006         0.078         0.429
##  WPUBT_B        0.014         0.009        -0.023         0.009         0.008
##  WPUBT_1        0.049         0.033        -0.014         0.006         0.023
##  WPUBT_2        0.036         0.050        -0.003        -0.027        -0.029
##  WPUBT_3        0.034         0.065        -0.001        -0.015        -0.031
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       1.000
##  WPUBT_B       -0.001         1.000
##  WPUBT_1       -0.005         0.259         1.000
##  WPUBT_2       -0.052         0.098         0.380         1.000
##  WPUBT_3       -0.037         0.040         0.154         0.405         1.000
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.029         0.000
##  RI_WCHRT       0.016         0.028         0.000
##  WINTT_B        0.000         0.000         0.000         0.000
##  WINTT_1        0.000         0.000         0.000         0.044         0.000
##  WINTT_2        0.000         0.000         0.000         0.009         0.030
##  WINTT_3        0.000         0.000         0.000         0.003         0.013
##  WWCHRT_B       0.000         0.000         0.000         0.031         0.037
##  WWCHRT_1       0.000         0.000         0.000         0.028         0.030
##  WWCHRT_2       0.000         0.000         0.000         0.006         0.028
##  WWCHRT_3       0.000         0.000         0.000         0.003         0.013
##  WPUBT_B        0.000         0.000         0.000         0.019         0.020
##  WPUBT_1        0.000         0.000         0.000         0.030         0.029
##  WPUBT_2        0.000         0.000         0.000         0.012         0.020
##  WPUBT_3        0.000         0.000         0.000         0.005         0.009
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.021         0.000
##  WWCHRT_B       0.007         0.003         0.000
##  WWCHRT_1       0.016         0.007         0.053         0.000
##  WWCHRT_2       0.018         0.018         0.009         0.032         0.000
##  WWCHRT_3       0.027         0.029         0.004         0.018         0.060
##  WPUBT_B        0.008         0.004         0.025         0.022         0.009
##  WPUBT_1        0.025         0.011         0.043         0.034         0.032
##  WPUBT_2        0.016         0.016         0.016         0.018         0.018
##  WPUBT_3        0.016         0.014         0.007         0.008         0.016
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.005         0.000
##  WPUBT_1        0.018         0.022         0.000
##  WPUBT_2        0.028         0.012         0.021         0.000
##  WPUBT_3        0.025         0.006         0.013         0.016         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT      999.000
##  RI_PUBTT       3.071       999.000
##  RI_WCHRT       9.599        12.263       999.000
##  WINTT_B        0.000         0.000         0.000       999.000
##  WINTT_1        0.000         0.000         0.000         1.164       999.000
##  WINTT_2        0.000         0.000         0.000         1.120         6.062
##  WINTT_3        0.000         0.000         0.000         0.992         5.123
##  WWCHRT_B       0.000         0.000         0.000        -1.672         0.681
##  WWCHRT_1       0.000         0.000         0.000        -1.898         0.233
##  WWCHRT_2       0.000         0.000         0.000        -1.115         1.672
##  WWCHRT_3       0.000         0.000         0.000        -1.110         1.547
##  WPUBT_B        0.000         0.000         0.000         0.753         0.484
##  WPUBT_1        0.000         0.000         0.000         0.077         0.201
##  WPUBT_2        0.000         0.000         0.000         0.204         0.053
##  WPUBT_3        0.000         0.000         0.000         0.273         0.350
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2      999.000
##  WINTT_3       17.618       999.000
##  WWCHRT_B       0.679         0.379       999.000
##  WWCHRT_1      -0.635         0.283        -1.616       999.000
##  WWCHRT_2       1.766         2.689        -1.584         5.586       999.000
##  WWCHRT_3       0.499         1.790        -1.559         4.222         7.175
##  WPUBT_B        1.754         2.519        -0.929         0.440         0.822
##  WPUBT_1        1.933         2.859        -0.317         0.181         0.718
##  WPUBT_2        2.238         3.200        -0.167        -1.484        -1.605
##  WPUBT_3        2.194         4.719        -0.108        -1.837        -1.943
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3     999.000
##  WPUBT_B       -0.109       999.000
##  WPUBT_1       -0.282        11.839       999.000
##  WPUBT_2       -1.841         8.299        18.529       999.000
##  WPUBT_3       -1.439         6.815        12.168        25.682       999.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.002         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.244         0.000
##  WINTT_2        1.000         1.000         1.000         0.263         0.000
##  WINTT_3        1.000         1.000         1.000         0.321         0.000
##  WWCHRT_B       1.000         1.000         1.000         0.095         0.496
##  WWCHRT_1       1.000         1.000         1.000         0.058         0.816
##  WWCHRT_2       1.000         1.000         1.000         0.265         0.095
##  WWCHRT_3       1.000         1.000         1.000         0.267         0.122
##  WPUBT_B        1.000         1.000         1.000         0.451         0.628
##  WPUBT_1        1.000         1.000         1.000         0.938         0.841
##  WPUBT_2        1.000         1.000         1.000         0.839         0.958
##  WPUBT_3        1.000         1.000         1.000         0.785         0.726
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.497         0.705         0.000
##  WWCHRT_1       0.526         0.777         0.106         0.000
##  WWCHRT_2       0.077         0.007         0.113         0.000         0.000
##  WWCHRT_3       0.618         0.073         0.119         0.000         0.000
##  WPUBT_B        0.080         0.012         0.353         0.660         0.411
##  WPUBT_1        0.053         0.004         0.751         0.857         0.472
##  WPUBT_2        0.025         0.001         0.867         0.138         0.108
##  WPUBT_3        0.028         0.000         0.914         0.066         0.052
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.913         0.000
##  WPUBT_1        0.778         0.000         0.000
##  WPUBT_2        0.066         0.000         0.000         0.000
##  WPUBT_3        0.150         0.000         0.000         0.000         0.000
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\all full model.dgm
## 
##      Beginning Time:  14:02:22
##         Ending Time:  14:02:23
##        Elapsed Time:  00:00:01
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Boys’ Model (No Covariates)

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/all full model boys.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024   2:18 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Full Sample Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3
##   intt_b intt_1
##   intt_2 intt_3
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   USEOBSERVATIONS ARE (Sex EQ 1);
## 
##   DEFINE:
##   wchrt_b = wchrt_b*10;
##   wchrt_1 = wchrt_1*10;
##   wchrt_2 = wchrt_2*10;
##   wchrt_3 = wchrt_3*10;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
##   RI_pubtT BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! RI correlations
##   RI_intt with RI_pubtT RI_wchrt;
##   RI_pubtT with RI_wchrt;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b;
##   wwchrt_1 ON wintt_b;
##   wwchrt_1 ON wpubt_b;
## 
##   wwchrt_2 ON wwchrt_1;
##   wwchrt_2 ON wintt_1;
##   wwchrt_2 ON wpubt_1;
## 
##   wwchrt_3 ON wwchrt_2;
##   wwchrt_3 ON wintt_2;
##   wwchrt_3 ON wpubt_2;
## 
##   wpubt_1 ON wpubt_b;
##   wpubt_1 ON wintt_b;
##   wpubt_1 ON wwchrt_b;
## 
##   wpubt_2 ON wpubt_1;
##   wpubt_2 ON wintt_1;
##   wpubt_2 ON wwchrt_1;
## 
##   wpubt_3 ON wpubt_2;
##   wpubt_3 ON wintt_2;
##   wpubt_3 ON wwchrt_2;
## 
##   wintt_1 ON wintt_b;
##   wintt_1 ON wpubt_b;
##   wintt_1 ON wwchrt_b;
## 
##   wintt_2 ON wintt_1;
##   wintt_2 ON wpubt_1;
##   wintt_2 ON wwchrt_1;
## 
##   wintt_3 ON wintt_2;
##   wintt_3 ON wpubt_2;
##   wintt_3 ON wwchrt_2;
## 
##   ! Estimate the covariance between the within-person
##   ! centered variables at the first wave
##   wintt_b with wpubt_b;
##   wwchrt_b with wintt_b wpubt_b;
## 
##   ! Estimate covariances between residuals of within-person components
##   ! (i.e., innovations)
##   wintt_1 with wpubt_1 wwchrt_1;
##   wpubt_1 with wwchrt_1;
## 
##   wintt_2 with wpubt_2 wwchrt_2;
##   wpubt_2 with wwchrt_2;
## 
##   wintt_3 with wpubt_3 wwchrt_3;
##   wpubt_3 with wwchrt_3;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
##   [pubt_b pubt_1 pubt_2 pubt_3];
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_intt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_pubtT with wwchrt_b@0 wintt_b@0 wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES Tech4;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  1
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Full Sample Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                        5417
## 
## Number of dependent variables                                   12
## Number of independent variables                                  0
## Number of continuous latent variables                           15
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3     INTT_B      INTT_1
##    INTT_2      INTT_3      PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_INTT     RI_PUBTT    RI_WCHRT    WINTT_B     WINTT_1     WINTT_2
##    WINTT_3     WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3    WPUBT_B
##    WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns           136
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3       INTT_B
##               ________      ________      ________      ________      ________
##  WCHRT_B        0.999
##  WCHRT_1        0.939         0.940
##  WCHRT_2        0.775         0.756         0.776
##  WCHRT_3        0.170         0.166         0.157         0.170
##  INTT_B         0.998         0.940         0.776         0.170         1.000
##  INTT_1         0.946         0.939         0.759         0.167         0.946
##  INTT_2         0.924         0.896         0.774         0.167         0.925
##  INTT_3         0.860         0.834         0.721         0.170         0.860
##  PUBT_B         0.884         0.832         0.697         0.162         0.884
##  PUBT_1         0.421         0.418         0.407         0.107         0.421
##  PUBT_2         0.906         0.880         0.759         0.164         0.907
##  PUBT_3         0.857         0.832         0.715         0.165         0.858
## 
## 
##            Covariance Coverage
##               INTT_1        INTT_2        INTT_3        PUBT_B        PUBT_1
##               ________      ________      ________      ________      ________
##  INTT_1         0.947
##  INTT_2         0.902         0.925
##  INTT_3         0.840         0.841         0.861
##  PUBT_B         0.838         0.820         0.765         0.885
##  PUBT_1         0.421         0.411         0.396         0.408         0.421
##  PUBT_2         0.885         0.903         0.823         0.807         0.406
##  PUBT_3         0.838         0.836         0.843         0.765         0.397
## 
## 
##            Covariance Coverage
##               PUBT_2        PUBT_3
##               ________      ________
##  PUBT_2         0.907
##  PUBT_3         0.823         0.858
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B               0.000       1.217      -1.812    0.02%      -0.540     -0.283     -0.150
##             5409.000       0.465       3.097       6.647    0.02%       0.008      0.483
##      WCHRT_1               0.000       1.555      -1.970    0.02%      -0.571     -0.305     -0.172
##             5092.000       0.518       7.309       8.991    0.02%      -0.006      0.536
##      WCHRT_2               0.000       1.809      -1.811    0.02%      -0.619     -0.332     -0.185
##             4203.000       0.601      10.489       9.219    0.02%       0.005      0.567
##      WCHRT_3               0.000       1.652      -1.326    0.11%      -0.664     -0.397     -0.240
##              921.000       0.702       6.257       7.060    0.11%      -0.031      0.640
##      INTT_B                0.000       2.404      -1.161    0.52%      -1.125     -1.092     -1.074
##             5415.000       3.170       7.582      13.915    0.02%      -0.132      0.893
##      INTT_1                0.000       2.317      -1.298    0.02%      -1.181     -1.088     -1.055
##             5129.000       3.320       6.509      12.777    0.02%      -0.181      0.878
##      INTT_2                0.000       2.332      -1.546    0.06%      -1.266     -1.119     -1.045
##             5013.000       3.804       6.777      13.867    0.02%      -0.281      0.867
##      INTT_3                0.000       2.032      -1.558    0.02%      -1.372     -1.263     -0.503
##             4662.000       4.011       4.776      13.693    0.02%      -0.328      0.792
##      PUBT_B                0.000       0.427      -0.967    0.29%      -0.933      0.043      0.053
##             4792.000       0.584      -0.183       3.081    0.02%       0.065      1.037
##      PUBT_1                0.000       0.315      -1.129    0.22%      -0.873     -0.069      0.021
##             2280.000       0.575      -0.570       3.082    0.04%       0.097      0.901
##      PUBT_2                0.000       0.068      -1.858    0.02%      -0.790     -0.210     -0.016
##             4915.000       0.621      -0.498       3.016    0.02%       0.178      0.725
##      PUBT_3                0.000      -0.198      -2.150    0.04%      -0.694     -0.112      0.040
##             4650.000       0.656      -0.272       2.534    0.04%       0.230      0.686
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       69
## 
## Loglikelihood
## 
##           H0 Value                      -68328.736
##           H0 Scaling Correction Factor      2.5100
##             for MLR
##           H1 Value                      -68283.222
##           H1 Scaling Correction Factor      2.2056
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  136795.472
##           Bayesian (BIC)                137250.685
##           Sample-Size Adjusted BIC      137031.425
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                             75.508*
##           Degrees of Freedom                    21
##           P-Value                           0.0000
##           Scaling Correction Factor         1.2055
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.022
##           90 Percent C.I.                    0.017  0.027
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.994
##           TLI                                0.980
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           8796.875
##           Degrees of Freedom                    66
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.014
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  RI_PUBTT BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.275      0.135     -2.034      0.042
##     WINTT_B           -0.011      0.015     -0.737      0.461
##     WPUBT_B           -0.038      0.021     -1.860      0.063
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.334      0.059      5.682      0.000
##     WINTT_1            0.026      0.013      2.027      0.043
##     WPUBT_1           -0.025      0.023     -1.073      0.283
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.502      0.050     10.106      0.000
##     WINTT_2           -0.024      0.012     -1.967      0.049
##     WPUBT_2           -0.087      0.025     -3.510      0.000
## 
##  WPUBT_1  ON
##     WPUBT_B            0.174      0.033      5.291      0.000
##     WINTT_B           -0.008      0.021     -0.369      0.712
##     WWCHRT_B           0.019      0.156      0.124      0.902
## 
##  WPUBT_2  ON
##     WPUBT_1            0.326      0.030     10.877      0.000
##     WINTT_1            0.015      0.014      1.101      0.271
##     WWCHRT_1          -0.069      0.037     -1.851      0.064
## 
##  WPUBT_3  ON
##     WPUBT_2            0.410      0.020     20.778      0.000
##     WINTT_2            0.008      0.010      0.862      0.389
##     WWCHRT_2          -0.064      0.026     -2.469      0.014
## 
##  WINTT_1  ON
##     WINTT_B            0.089      0.052      1.704      0.088
##     WPUBT_B           -0.024      0.039     -0.621      0.534
##     WWCHRT_B           0.287      0.229      1.253      0.210
## 
##  WINTT_2  ON
##     WINTT_1            0.196      0.047      4.196      0.000
##     WPUBT_1           -0.029      0.058     -0.499      0.617
##     WWCHRT_1           0.122      0.074      1.655      0.098
## 
##  WINTT_3  ON
##     WINTT_2            0.337      0.034      9.962      0.000
##     WPUBT_2            0.008      0.037      0.210      0.834
##     WWCHRT_2           0.110      0.063      1.764      0.078
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.047      0.017      2.786      0.005
##     RI_WCHRT           0.120      0.018      6.489      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.059      0.007      8.497      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B           -0.004      0.019     -0.195      0.845
##     WWCHRT_B          -0.017      0.015     -1.161      0.246
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B           -0.023      0.008     -2.954      0.003
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1           -0.051      0.025     -2.021      0.043
##     WWCHRT_1           0.035      0.022      1.643      0.100
## 
##  WPUBT_1  WITH
##     WWCHRT_1          -0.007      0.015     -0.473      0.636
## 
##  WINTT_2  WITH
##     WPUBT_2           -0.015      0.017     -0.861      0.389
##     WWCHRT_2           0.011      0.014      0.784      0.433
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.022      0.006     -3.855      0.000
## 
##  WINTT_3  WITH
##     WPUBT_3            0.029      0.016      1.863      0.063
##     WWCHRT_3          -0.002      0.027     -0.079      0.937
## 
##  WPUBT_3  WITH
##     WWCHRT_3          -0.013      0.010     -1.328      0.184
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.009      0.032      0.974
##     WCHRT_1            0.007      0.010      0.681      0.496
##     WCHRT_2            0.014      0.011      1.269      0.204
##     WCHRT_3           -0.060      0.018     -3.274      0.001
##     INTT_B             0.001      0.024      0.021      0.983
##     INTT_1             0.010      0.025      0.413      0.679
##     INTT_2             0.010      0.027      0.381      0.703
##     INTT_3             0.012      0.029      0.403      0.687
##     PUBT_B             0.002      0.011      0.146      0.884
##     PUBT_1             0.019      0.015      1.248      0.212
##     PUBT_2             0.003      0.011      0.242      0.809
##     PUBT_3             0.003      0.012      0.224      0.823
## 
##  Variances
##     RI_INTT            1.941      0.095     20.370      0.000
##     RI_PUBTT           0.099      0.012      8.589      0.000
##     RI_WCHRT           0.388      0.013     28.904      0.000
##     WINTT_B            1.306      0.097     13.443      0.000
##     WWCHRT_B           0.077      0.010      7.532      0.000
##     WPUBT_B            0.492      0.015     32.328      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.286      0.090     14.229      0.000
##     WINTT_2            1.803      0.096     18.699      0.000
##     WINTT_3            1.919      0.083     23.002      0.000
##     WWCHRT_1           0.125      0.022      5.585      0.000
##     WWCHRT_2           0.227      0.031      7.451      0.000
##     WWCHRT_3           0.211      0.050      4.222      0.000
##     WPUBT_1            0.458      0.016     28.440      0.000
##     WPUBT_2            0.467      0.012     40.479      0.000
##     WPUBT_3            0.465      0.011     42.516      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.151E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.773      0.014     55.578      0.000
##     INTT_1             0.774      0.015     50.259      0.000
##     INTT_2             0.715      0.013     54.953      0.000
##     INTT_3             0.690      0.012     55.719      0.000
## 
##  RI_PUBTT BY
##     PUBT_B             0.410      0.024     17.332      0.000
##     PUBT_1             0.417      0.025     16.424      0.000
##     PUBT_2             0.401      0.023     17.134      0.000
##     PUBT_3             0.390      0.023     17.329      0.000
## 
##  RI_WCHRT BY
##     WCHRT_B            0.914      0.011     82.570      0.000
##     WCHRT_1            0.865      0.018     48.121      0.000
##     WCHRT_2            0.784      0.021     37.561      0.000
##     WCHRT_3            0.763      0.026     29.123      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.634      0.017     37.389      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.634      0.019     33.728      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.699      0.013     52.587      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.724      0.012     61.269      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.406      0.025     16.320      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.502      0.031     16.201      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.621      0.026     23.580      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.647      0.031     20.967      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.912      0.011     85.663      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.909      0.012     78.101      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.916      0.010     89.268      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.921      0.010     96.629      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.210      0.102     -2.053      0.040
##     WINTT_B           -0.035      0.047     -0.732      0.464
##     WPUBT_B           -0.074      0.040     -1.858      0.063
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.244      0.047      5.167      0.000
##     WINTT_1            0.060      0.032      1.913      0.056
##     WPUBT_1           -0.034      0.031     -1.093      0.275
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.469      0.076      6.150      0.000
##     WINTT_2           -0.061      0.031     -1.953      0.051
##     WPUBT_2           -0.118      0.032     -3.703      0.000
## 
##  WPUBT_1  ON
##     WPUBT_B            0.177      0.033      5.429      0.000
##     WINTT_B           -0.013      0.035     -0.370      0.712
##     WWCHRT_B           0.008      0.063      0.124      0.902
## 
##  WPUBT_2  ON
##     WPUBT_1            0.311      0.029     10.681      0.000
##     WINTT_1            0.024      0.022      1.099      0.272
##     WWCHRT_1          -0.035      0.018     -1.901      0.057
## 
##  WPUBT_3  ON
##     WPUBT_2            0.397      0.018     21.486      0.000
##     WINTT_2            0.015      0.018      0.862      0.389
##     WWCHRT_2          -0.042      0.017     -2.544      0.011
## 
##  WINTT_1  ON
##     WINTT_B            0.089      0.052      1.726      0.084
##     WPUBT_B           -0.015      0.024     -0.621      0.534
##     WWCHRT_B           0.070      0.055      1.264      0.206
## 
##  WINTT_2  ON
##     WINTT_1            0.164      0.040      4.103      0.000
##     WPUBT_1           -0.015      0.029     -0.499      0.618
##     WWCHRT_1           0.032      0.019      1.672      0.095
## 
##  WINTT_3  ON
##     WINTT_2            0.314      0.030     10.348      0.000
##     WPUBT_2            0.004      0.018      0.210      0.834
##     WWCHRT_2           0.037      0.020      1.825      0.068
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.107      0.039      2.748      0.006
##     RI_WCHRT           0.138      0.020      6.835      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.301      0.041      7.394      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B           -0.005      0.023     -0.195      0.845
##     WWCHRT_B          -0.055      0.049     -1.134      0.257
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B           -0.117      0.040     -2.901      0.004
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1           -0.067      0.033     -2.027      0.043
##     WWCHRT_1           0.088      0.053      1.660      0.097
## 
##  WPUBT_1  WITH
##     WWCHRT_1          -0.030      0.063     -0.474      0.635
## 
##  WINTT_2  WITH
##     WPUBT_2           -0.016      0.018     -0.861      0.389
##     WWCHRT_2           0.017      0.022      0.769      0.442
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.068      0.016     -4.176      0.000
## 
##  WINTT_3  WITH
##     WPUBT_3            0.031      0.017      1.867      0.062
##     WWCHRT_3          -0.003      0.043     -0.079      0.937
## 
##  WPUBT_3  WITH
##     WWCHRT_3          -0.042      0.033     -1.285      0.199
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.014      0.032      0.974
##     WCHRT_1            0.009      0.014      0.686      0.493
##     WCHRT_2            0.018      0.014      1.291      0.197
##     WCHRT_3           -0.074      0.024     -3.061      0.002
##     INTT_B             0.000      0.013      0.021      0.983
##     INTT_1             0.006      0.014      0.416      0.678
##     INTT_2             0.005      0.014      0.383      0.702
##     INTT_3             0.006      0.014      0.406      0.685
##     PUBT_B             0.002      0.014      0.146      0.884
##     PUBT_1             0.025      0.020      1.253      0.210
##     PUBT_2             0.003      0.014      0.242      0.809
##     PUBT_3             0.003      0.014      0.224      0.823
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     RI_PUBTT           1.000      0.000    999.000    999.000
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.987      0.013     76.375      0.000
##     WINTT_2            0.971      0.013     73.019      0.000
##     WINTT_3            0.899      0.019     46.956      0.000
##     WWCHRT_1           0.953      0.043     22.395      0.000
##     WWCHRT_2           0.932      0.024     38.293      0.000
##     WWCHRT_3           0.756      0.073     10.408      0.000
##     WPUBT_1            0.969      0.011     84.887      0.000
##     WPUBT_2            0.902      0.018     49.951      0.000
##     WPUBT_3            0.838      0.015     57.068      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.013      0.013      0.975      0.329
##     WINTT_2            0.029      0.013      2.209      0.027
##     WINTT_3            0.101      0.019      5.271      0.000
##     WWCHRT_1           0.047      0.043      1.093      0.274
##     WWCHRT_2           0.068      0.024      2.773      0.006
##     WWCHRT_3           0.244      0.073      3.366      0.001
##     WPUBT_1            0.031      0.011      2.745      0.006
##     WPUBT_2            0.098      0.018      5.447      0.000
##     WPUBT_3            0.162      0.015     11.017      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_INTT  BY INTT_B                24.005    -0.161     -0.224       -0.124
## RI_INTT  BY INTT_1                20.965     0.124      0.172        0.096
## RI_PUBTT BY PUBT_B                17.862    -0.675     -0.213       -0.277
## RI_WCHRT BY PUBT_B                14.496    -0.128     -0.080       -0.104
## WINTT_B  BY INTT_3                26.678    -0.154     -0.175       -0.087
## WINTT_1  BY INTT_2                23.076    -0.444     -0.506       -0.260
## WINTT_1  BY INTT_3                24.885     0.157      0.179        0.089
## WINTT_3  BY INTT_B                30.637    -0.117     -0.171       -0.095
## WINTT_3  BY INTT_1                26.270     0.099      0.145        0.080
## WINTT_3  BY INTT_2                24.723    -0.721     -1.054       -0.541
## WWCHRT_2 BY PUBT_B                12.726    -0.137     -0.068       -0.088
## WWCHRT_2 BY PUBT_1                12.966     0.778      0.384        0.508
## WPUBT_B  BY WCHRT_1               13.527     0.199      0.140        0.194
## WPUBT_B  BY WCHRT_2               10.433    -0.053     -0.037       -0.046
## 
## ON/BY Statements
## 
## RI_INTT  ON WINTT_B  /
## WINTT_B  BY RI_INTT               25.384    -0.269     -0.221       -0.221
## RI_INTT  ON WINTT_1  /
## WINTT_1  BY RI_INTT               25.529     0.239      0.196        0.196
## RI_PUBTT ON WWCHRT_2 /
## WWCHRT_2 BY RI_PUBTT              12.668    -0.166     -0.260       -0.260
## RI_WCHRT ON WPUBT_B  /
## WPUBT_B  BY RI_WCHRT              13.418    -0.101     -0.114       -0.114
## WINTT_B  ON RI_INTT  /
## RI_INTT  BY WINTT_B               24.136    -0.179     -0.218       -0.218
## WINTT_B  ON WINTT_3  /
## WINTT_3  BY WINTT_B               30.051    -0.125     -0.160       -0.160
## WINTT_1  ON RI_INTT  /
## RI_INTT  BY WINTT_1               25.658     0.150      0.183        0.183
## WINTT_1  ON WINTT_3  /
## WINTT_3  BY WINTT_1               26.135     0.102      0.131        0.131
## WINTT_2  ON WINTT_3  /
## WINTT_3  BY WINTT_2               24.725    -0.721     -0.773       -0.773
## WINTT_3  ON WINTT_B  /
## WINTT_B  BY WINTT_3               26.678    -0.154     -0.120       -0.120
## WINTT_3  ON WINTT_1  /
## WINTT_1  BY WINTT_3               24.885     0.157      0.122        0.122
## WWCHRT_2 ON WPUBT_B  /
## WPUBT_B  BY WWCHRT_2              11.942    -0.064     -0.090       -0.090
## WPUBT_B  ON RI_PUBTT /
## RI_PUBTT BY WPUBT_B               17.655    -0.750     -0.337       -0.337
## WPUBT_B  ON RI_WCHRT /
## RI_WCHRT BY WPUBT_B               14.641    -0.134     -0.120       -0.120
## WPUBT_B  ON WWCHRT_2 /
## WWCHRT_2 BY WPUBT_B               12.701    -0.142     -0.100       -0.100
## WPUBT_1  ON WWCHRT_2 /
## WWCHRT_2 BY WPUBT_1               12.967     0.778      0.559        0.559
## 
## WITH Statements
## 
## INTT_2   WITH INTT_1              27.249    -0.580     -0.580      999.000
## INTT_3   WITH INTT_B              28.259    -0.195     -0.195      999.000
## INTT_3   WITH INTT_1              26.918     0.193      0.193      999.000
## INTT_3   WITH INTT_2              25.155    -1.397     -1.397      999.000
## PUBT_B   WITH WCHRT_1             13.803     0.096      0.096      999.000
## PUBT_B   WITH WCHRT_2             10.751    -0.026     -0.026      999.000
## PUBT_1   WITH WCHRT_1             13.852    -0.362     -0.362      999.000
## PUBT_2   WITH PUBT_1              12.010    -0.098     -0.098      999.000
## WINTT_B  WITH RI_INTT             26.249    -0.360     -0.226       -0.226
## WINTT_1  WITH RI_INTT             25.925     0.290      0.183        0.183
## WINTT_3  WITH WINTT_B             26.970    -0.202     -0.128       -0.128
## WINTT_3  WITH WINTT_1             26.784     0.199      0.127        0.127
## WINTT_3  WITH WINTT_2             25.157    -1.397     -0.751       -0.751
## WPUBT_B  WITH RI_WCHRT            14.009    -0.051     -0.117       -0.117
## WPUBT_B  WITH WWCHRT_2            12.087    -0.031     -0.094       -0.094
## WPUBT_1  WITH WWCHRT_2            12.337     0.173      0.535        0.535
## 
## Variances/Residual Variances
## 
## INTT_2                            22.727     3.899      3.899        1.026
## 
## 
## TECHNICAL 4 OUTPUT
## 
## 
##      ESTIMATES DERIVED FROM THE MODEL
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.941
##  RI_PUBTT       0.047         0.099
##  RI_WCHRT       0.120         0.059         0.388
##  WINTT_B        0.000         0.000         0.000         1.306
##  WINTT_1        0.000         0.000         0.000         0.111         1.303
##  WINTT_2        0.000         0.000         0.000         0.021         0.261
##  WINTT_3        0.000         0.000         0.000         0.007         0.093
##  WWCHRT_B       0.000         0.000         0.000        -0.017         0.021
##  WWCHRT_1       0.000         0.000         0.000        -0.009         0.029
##  WWCHRT_2       0.000         0.000         0.000         0.000         0.045
##  WWCHRT_3       0.000         0.000         0.000         0.000         0.017
##  WPUBT_B        0.000         0.000         0.000        -0.004        -0.019
##  WPUBT_1        0.000         0.000         0.000        -0.011        -0.055
##  WPUBT_2        0.000         0.000         0.000        -0.001         0.000
##  WPUBT_3        0.000         0.000         0.000         0.000        -0.001
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.858
##  WINTT_3        0.628         2.135
##  WWCHRT_B       0.002         0.000         0.077
##  WWCHRT_1       0.022         0.012        -0.020         0.131
##  WWCHRT_2       0.026         0.035        -0.006         0.045         0.244
##  WWCHRT_3      -0.029         0.001        -0.003         0.023         0.124
##  WPUBT_B       -0.008        -0.003        -0.023        -0.013        -0.007
##  WPUBT_1       -0.026        -0.009        -0.002        -0.010        -0.016
##  WPUBT_2       -0.020        -0.006         0.001        -0.012        -0.030
##  WPUBT_3        0.005         0.030         0.001        -0.007        -0.028
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.280
##  WPUBT_B       -0.006         0.492
##  WPUBT_1       -0.021         0.085         0.473
##  WPUBT_2       -0.060         0.028         0.154         0.518
##  WPUBT_3       -0.046         0.012         0.064         0.214         0.555
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.095
##  RI_PUBTT       0.017         0.012
##  RI_WCHRT       0.018         0.007         0.013
##  WINTT_B        0.000         0.000         0.000         0.097
##  WINTT_1        0.000         0.000         0.000         0.073         0.101
##  WINTT_2        0.000         0.000         0.000         0.017         0.072
##  WINTT_3        0.000         0.000         0.000         0.006         0.029
##  WWCHRT_B       0.000         0.000         0.000         0.015         0.018
##  WWCHRT_1       0.000         0.000         0.000         0.016         0.018
##  WWCHRT_2       0.000         0.000         0.000         0.006         0.021
##  WWCHRT_3       0.000         0.000         0.000         0.003         0.011
##  WPUBT_B        0.000         0.000         0.000         0.019         0.020
##  WPUBT_1        0.000         0.000         0.000         0.028         0.028
##  WPUBT_2        0.000         0.000         0.000         0.010         0.021
##  WPUBT_3        0.000         0.000         0.000         0.004         0.010
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.108
##  WINTT_3        0.082         0.109
##  WWCHRT_B       0.004         0.002         0.010
##  WWCHRT_1       0.011         0.005         0.009         0.020
##  WWCHRT_2       0.016         0.017         0.003         0.011         0.032
##  WWCHRT_3       0.024         0.032         0.002         0.006         0.021
##  WPUBT_B        0.007         0.003         0.008         0.008         0.004
##  WPUBT_1        0.030         0.013         0.012         0.013         0.014
##  WPUBT_2        0.022         0.023         0.004         0.006         0.008
##  WPUBT_3        0.021         0.021         0.002         0.003         0.007
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.045
##  WPUBT_B        0.002         0.015
##  WPUBT_1        0.008         0.017         0.019
##  WPUBT_2        0.013         0.007         0.018         0.015
##  WPUBT_3        0.012         0.003         0.009         0.014         0.016
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT       20.370
##  RI_PUBTT       2.786         8.589
##  RI_WCHRT       6.489         8.497        28.904
##  WINTT_B        0.000         0.000         0.000        13.443
##  WINTT_1        0.000         0.000         0.000         1.526        12.927
##  WINTT_2        0.000         0.000         0.000         1.247         3.623
##  WINTT_3        0.000         0.000         0.000         1.167         3.186
##  WWCHRT_B       0.000         0.000         0.000        -1.161         1.163
##  WWCHRT_1       0.000         0.000         0.000        -0.599         1.591
##  WWCHRT_2       0.000         0.000         0.000         0.007         2.141
##  WWCHRT_3       0.000         0.000         0.000        -0.108         1.468
##  WPUBT_B        0.000         0.000         0.000        -0.195        -0.959
##  WPUBT_1        0.000         0.000         0.000        -0.395        -1.957
##  WPUBT_2        0.000         0.000         0.000        -0.133        -0.011
##  WPUBT_3        0.000         0.000         0.000        -0.088        -0.083
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2       17.168
##  WINTT_3        7.710        19.542
##  WWCHRT_B       0.419        -0.045         7.532
##  WWCHRT_1       2.001         2.367        -2.251         6.510
##  WWCHRT_2       1.568         2.079        -2.008         3.968         7.664
##  WWCHRT_3      -1.201         0.041        -1.927         3.572         5.817
##  WPUBT_B       -1.067        -1.029        -2.954        -1.501        -1.644
##  WPUBT_1       -0.847        -0.711        -0.186        -0.741        -1.169
##  WPUBT_2       -0.944        -0.265         0.226        -1.920        -3.698
##  WPUBT_3        0.256         1.411         0.447        -2.499        -3.756
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       6.170
##  WPUBT_B       -2.326        32.328
##  WPUBT_1       -2.486         4.910        24.459
##  WPUBT_2       -4.423         3.906         8.665        33.835
##  WPUBT_3       -3.687         3.582         7.025        15.244        35.011
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.005         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.127         0.000
##  WINTT_2        1.000         1.000         1.000         0.212         0.000
##  WINTT_3        1.000         1.000         1.000         0.243         0.001
##  WWCHRT_B       1.000         1.000         1.000         0.246         0.245
##  WWCHRT_1       1.000         1.000         1.000         0.549         0.112
##  WWCHRT_2       1.000         1.000         1.000         0.994         0.032
##  WWCHRT_3       1.000         1.000         1.000         0.914         0.142
##  WPUBT_B        1.000         1.000         1.000         0.845         0.337
##  WPUBT_1        1.000         1.000         1.000         0.693         0.050
##  WPUBT_2        1.000         1.000         1.000         0.894         0.991
##  WPUBT_3        1.000         1.000         1.000         0.930         0.934
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.676         0.964         0.000
##  WWCHRT_1       0.045         0.018         0.024         0.000
##  WWCHRT_2       0.117         0.038         0.045         0.000         0.000
##  WWCHRT_3       0.230         0.968         0.054         0.000         0.000
##  WPUBT_B        0.286         0.303         0.003         0.133         0.100
##  WPUBT_1        0.397         0.477         0.852         0.458         0.242
##  WPUBT_2        0.345         0.791         0.821         0.055         0.000
##  WPUBT_3        0.798         0.158         0.655         0.012         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.020         0.000
##  WPUBT_1        0.013         0.000         0.000
##  WPUBT_2        0.000         0.000         0.000         0.000
##  WPUBT_3        0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.000
##  RI_PUBTT       0.107         1.000
##  RI_WCHRT       0.138         0.301         1.000
##  WINTT_B        0.000         0.000         0.000         1.000
##  WINTT_1        0.000         0.000         0.000         0.085         1.000
##  WINTT_2        0.000         0.000         0.000         0.014         0.168
##  WINTT_3        0.000         0.000         0.000         0.004         0.056
##  WWCHRT_B       0.000         0.000         0.000        -0.055         0.067
##  WWCHRT_1       0.000         0.000         0.000        -0.023         0.071
##  WWCHRT_2       0.000         0.000         0.000         0.000         0.080
##  WWCHRT_3       0.000         0.000         0.000        -0.001         0.027
##  WPUBT_B        0.000         0.000         0.000        -0.005        -0.023
##  WPUBT_1        0.000         0.000         0.000        -0.014        -0.070
##  WPUBT_2        0.000         0.000         0.000        -0.002         0.000
##  WPUBT_3        0.000         0.000         0.000         0.000        -0.001
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.000
##  WINTT_3        0.316         1.000
##  WWCHRT_B       0.005         0.000         1.000
##  WWCHRT_1       0.045         0.023        -0.200         1.000
##  WWCHRT_2       0.038         0.049        -0.044         0.250         1.000
##  WWCHRT_3      -0.040         0.002        -0.022         0.120         0.476
##  WPUBT_B       -0.008        -0.003        -0.117        -0.050        -0.020
##  WPUBT_1       -0.027        -0.009        -0.012        -0.039        -0.048
##  WPUBT_2       -0.021        -0.006         0.005        -0.045        -0.084
##  WPUBT_3        0.005         0.028         0.004        -0.028        -0.075
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       1.000
##  WPUBT_B       -0.015         1.000
##  WPUBT_1       -0.058         0.176         1.000
##  WPUBT_2       -0.156         0.056         0.311         1.000
##  WPUBT_3       -0.116         0.023         0.125         0.400         1.000
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.039         0.000
##  RI_WCHRT       0.020         0.041         0.000
##  WINTT_B        0.000         0.000         0.000         0.000
##  WINTT_1        0.000         0.000         0.000         0.052         0.000
##  WINTT_2        0.000         0.000         0.000         0.011         0.040
##  WINTT_3        0.000         0.000         0.000         0.004         0.016
##  WWCHRT_B       0.000         0.000         0.000         0.049         0.056
##  WWCHRT_1       0.000         0.000         0.000         0.038         0.043
##  WWCHRT_2       0.000         0.000         0.000         0.011         0.038
##  WWCHRT_3       0.000         0.000         0.000         0.005         0.019
##  WPUBT_B        0.000         0.000         0.000         0.023         0.024
##  WPUBT_1        0.000         0.000         0.000         0.036         0.036
##  WPUBT_2        0.000         0.000         0.000         0.012         0.026
##  WPUBT_3        0.000         0.000         0.000         0.005         0.011
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.030         0.000
##  WWCHRT_B       0.011         0.004         0.000
##  WWCHRT_1       0.022         0.009         0.100         0.000
##  WWCHRT_2       0.025         0.024         0.024         0.048         0.000
##  WWCHRT_3       0.034         0.041         0.012         0.030         0.076
##  WPUBT_B        0.007         0.003         0.040         0.033         0.011
##  WPUBT_1        0.032         0.013         0.065         0.052         0.040
##  WPUBT_2        0.022         0.022         0.021         0.023         0.021
##  WPUBT_3        0.021         0.019         0.009         0.011         0.019
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.006         0.000
##  WPUBT_1        0.023         0.032         0.000
##  WPUBT_2        0.034         0.013         0.029         0.000
##  WPUBT_3        0.033         0.006         0.015         0.018         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT      999.000
##  RI_PUBTT       2.748       999.000
##  RI_WCHRT       6.835         7.394       999.000
##  WINTT_B        0.000         0.000         0.000       999.000
##  WINTT_1        0.000         0.000         0.000         1.651       999.000
##  WINTT_2        0.000         0.000         0.000         1.283         4.216
##  WINTT_3        0.000         0.000         0.000         1.191         3.546
##  WWCHRT_B       0.000         0.000         0.000        -1.134         1.185
##  WWCHRT_1       0.000         0.000         0.000        -0.592         1.634
##  WWCHRT_2       0.000         0.000         0.000         0.007         2.090
##  WWCHRT_3       0.000         0.000         0.000        -0.108         1.455
##  WPUBT_B        0.000         0.000         0.000        -0.195        -0.963
##  WPUBT_1        0.000         0.000         0.000        -0.395        -1.966
##  WPUBT_2        0.000         0.000         0.000        -0.133        -0.011
##  WPUBT_3        0.000         0.000         0.000        -0.088        -0.083
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2      999.000
##  WINTT_3       10.416       999.000
##  WWCHRT_B       0.421        -0.045       999.000
##  WWCHRT_1       2.029         2.481        -1.990       999.000
##  WWCHRT_2       1.513         2.012        -1.858         5.245       999.000
##  WWCHRT_3      -1.201         0.040        -1.793         4.027         6.253
##  WPUBT_B       -1.071        -1.033        -2.901        -1.521        -1.715
##  WPUBT_1       -0.848        -0.712        -0.186        -0.744        -1.191
##  WPUBT_2       -0.943        -0.265         0.226        -1.928        -4.067
##  WPUBT_3        0.256         1.412         0.446        -2.606        -3.921
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3     999.000
##  WPUBT_B       -2.379       999.000
##  WPUBT_1       -2.527         5.509       999.000
##  WPUBT_2       -4.598         4.216        10.755       999.000
##  WPUBT_3       -3.551         3.825         8.321        21.768       999.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.006         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.099         0.000
##  WINTT_2        1.000         1.000         1.000         0.199         0.000
##  WINTT_3        1.000         1.000         1.000         0.233         0.000
##  WWCHRT_B       1.000         1.000         1.000         0.257         0.236
##  WWCHRT_1       1.000         1.000         1.000         0.554         0.102
##  WWCHRT_2       1.000         1.000         1.000         0.994         0.037
##  WWCHRT_3       1.000         1.000         1.000         0.914         0.146
##  WPUBT_B        1.000         1.000         1.000         0.845         0.336
##  WPUBT_1        1.000         1.000         1.000         0.693         0.049
##  WPUBT_2        1.000         1.000         1.000         0.894         0.991
##  WPUBT_3        1.000         1.000         1.000         0.930         0.934
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.674         0.964         0.000
##  WWCHRT_1       0.043         0.013         0.047         0.000
##  WWCHRT_2       0.130         0.044         0.063         0.000         0.000
##  WWCHRT_3       0.230         0.968         0.073         0.000         0.000
##  WPUBT_B        0.284         0.301         0.004         0.128         0.086
##  WPUBT_1        0.396         0.476         0.852         0.457         0.234
##  WPUBT_2        0.346         0.791         0.822         0.054         0.000
##  WPUBT_3        0.798         0.158         0.656         0.009         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.017         0.000
##  WPUBT_1        0.012         0.000         0.000
##  WPUBT_2        0.000         0.000         0.000         0.000
##  WPUBT_3        0.000         0.000         0.000         0.000         0.000
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\all full model boys.dgm
## 
##      Beginning Time:  14:18:22
##         Ending Time:  14:18:23
##        Elapsed Time:  00:00:01
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Girls’ Model (No Covariates)

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/all full model girls.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/01/2024   2:24 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Full Sample Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3
##   intt_b intt_1
##   intt_2 intt_3
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   USEOBSERVATIONS ARE (Sex EQ 2);
## 
##   DEFINE:
##   wchrt_b = wchrt_b*10;
##   wchrt_1 = wchrt_1*10;
##   wchrt_2 = wchrt_2*10;
##   wchrt_3 = wchrt_3*10;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
##   COVERAGE = 0;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
##   RI_pubtT BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! RI correlations
##   RI_intt with RI_pubtT RI_wchrt;
##   RI_pubtT with RI_wchrt;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b;
##   wwchrt_1 ON wintt_b;
##   wwchrt_1 ON wpubt_b;
## 
##   wwchrt_2 ON wwchrt_1;
##   wwchrt_2 ON wintt_1;
##   wwchrt_2 ON wpubt_1;
## 
##   wwchrt_3 ON wwchrt_2;
##   wwchrt_3 ON wintt_2;
##   wwchrt_3 ON wpubt_2;
## 
##   wpubt_1 ON wpubt_b;
##   wpubt_1 ON wintt_b;
##   wpubt_1 ON wwchrt_b;
## 
##   wpubt_2 ON wpubt_1;
##   wpubt_2 ON wintt_1;
##   wpubt_2 ON wwchrt_1;
## 
##   wpubt_3 ON wpubt_2;
##   wpubt_3 ON wintt_2;
##   wpubt_3 ON wwchrt_2;
## 
##   wintt_1 ON wintt_b;
##   wintt_1 ON wpubt_b;
##   wintt_1 ON wwchrt_b;
## 
##   wintt_2 ON wintt_1;
##   wintt_2 ON wpubt_1;
##   wintt_2 ON wwchrt_1;
## 
##   wintt_3 ON wintt_2;
##   wintt_3 ON wpubt_2;
##   wintt_3 ON wwchrt_2;
## 
##   ! Estimate the covariance between the within-person
##   ! centered variables at the first wave
##   wintt_b with wpubt_b;
##   wwchrt_b with wintt_b wpubt_b;
## 
##   ! Estimate covariances between residuals of within-person components
##   ! (i.e., innovations)
##   wintt_1 with wpubt_1 wwchrt_1;
##   wpubt_1 with wwchrt_1;
## 
##   wintt_2 with wpubt_2 wwchrt_2;
##   wpubt_2 with wwchrt_2;
## 
##   wintt_3 with wpubt_3 wwchrt_3;
##   wpubt_3 with wwchrt_3;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
##   [pubt_b pubt_1 pubt_2 pubt_3];
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_intt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_pubtT with wwchrt_b@0 wintt_b@0 wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES Tech4;
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Full Sample Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                        4945
## 
## Number of dependent variables                                   12
## Number of independent variables                                  0
## Number of continuous latent variables                           15
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3     INTT_B      INTT_1
##    INTT_2      INTT_3      PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_INTT     RI_PUBTT    RI_WCHRT    WINTT_B     WINTT_1     WINTT_2
##    WINTT_3     WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3    WPUBT_B
##    WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns           177
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.000
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3       INTT_B
##               ________      ________      ________      ________      ________
##  WCHRT_B        0.998
##  WCHRT_1        0.932         0.934
##  WCHRT_2        0.749         0.735         0.751
##  WCHRT_3        0.168         0.166         0.149         0.168
##  INTT_B         0.997         0.933         0.751         0.168         0.999
##  INTT_1         0.939         0.933         0.738         0.167         0.940
##  INTT_2         0.909         0.885         0.750         0.166         0.911
##  INTT_3         0.839         0.818         0.697         0.167         0.840
##  PUBT_B         0.721         0.675         0.549         0.135         0.722
##  PUBT_1         0.393         0.390         0.376         0.097         0.393
##  PUBT_2         0.837         0.816         0.691         0.151         0.838
##  PUBT_3         0.795         0.775         0.663         0.158         0.797
## 
## 
##            Covariance Coverage
##               INTT_1        INTT_2        INTT_3        PUBT_B        PUBT_1
##               ________      ________      ________      ________      ________
##  INTT_1         0.941
##  INTT_2         0.891         0.911
##  INTT_3         0.825         0.825         0.841
##  PUBT_B         0.680         0.658         0.608         0.722
##  PUBT_1         0.393         0.383         0.371         0.324         0.393
##  PUBT_2         0.821         0.833         0.763         0.612         0.363
##  PUBT_3         0.781         0.781         0.779         0.582         0.360
## 
## 
##            Covariance Coverage
##               PUBT_2        PUBT_3
##               ________      ________
##  PUBT_2         0.839
##  PUBT_3         0.742         0.797
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B               0.000       1.391      -2.415    0.02%      -0.570     -0.295     -0.135
##             4933.000       0.511       6.535       8.909    0.02%       0.028      0.527
##      WCHRT_1               0.000       2.461      -2.125    0.02%      -0.604     -0.310     -0.156
##             4619.000       0.620      18.861       9.968    0.02%       0.022      0.535
##      WCHRT_2               0.000       1.178      -2.197    0.03%      -0.629     -0.316     -0.159
##             3714.000       0.593       2.459       5.400    0.03%       0.026      0.561
##      WCHRT_3               0.000       1.793      -1.493    0.12%      -0.700     -0.340     -0.195
##              833.000       0.740       8.350       7.699    0.12%       0.013      0.633
##      INTT_B                0.000       2.649      -0.957    0.65%      -0.936     -0.919     -0.910
##             4940.000       2.589       8.798      12.062    0.02%       0.047      1.051
##      INTT_1                0.000       2.539      -1.190    0.02%      -1.081     -1.008     -0.979
##             4651.000       2.957       8.235      12.912    0.02%      -0.103      0.926
##      INTT_2                0.000       2.396      -1.697    0.02%      -1.274     -1.101     -1.005
##             4506.000       3.880       7.376      15.034    0.02%      -0.293      0.861
##      INTT_3                0.000       2.164      -1.822    0.05%      -1.562     -1.425     -0.672
##             4157.000       5.289       5.509      13.575    0.02%      -0.480      1.383
##      PUBT_B                0.000      -0.158      -1.606    0.20%      -0.981     -0.236      0.048
##             3571.000       0.743      -0.973       2.934    0.03%       0.480      0.792
##      PUBT_1                0.000      -0.349      -2.124    0.10%      -0.766     -0.044      0.115
##             1944.000       0.706      -0.284       2.830    0.05%       0.274      0.711
##      PUBT_2                0.000      -0.735      -2.839    0.02%      -0.533     -0.074      0.079
##             4149.000       0.574       0.946       2.308    0.02%       0.237      0.620
##      PUBT_3                0.000      -1.011      -2.940    0.03%      -0.528      0.032      0.142
##             3942.000       0.429       2.273       1.664    0.03%       0.252      0.472
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       69
## 
## Loglikelihood
## 
##           H0 Value                      -60645.783
##           H0 Scaling Correction Factor      2.5762
##             for MLR
##           H1 Value                      -60581.827
##           H1 Scaling Correction Factor      2.2701
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  121429.565
##           Bayesian (BIC)                121878.488
##           Sample-Size Adjusted BIC      121659.231
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                            101.154*
##           Degrees of Freedom                    21
##           P-Value                           0.0000
##           Scaling Correction Factor         1.2645
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.028
##           90 Percent C.I.                    0.022  0.033
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.989
##           TLI                                0.967
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           7651.364
##           Degrees of Freedom                    66
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.019
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  RI_PUBTT BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.049      0.079     -0.627      0.530
##     WINTT_B           -0.039      0.021     -1.860      0.063
##     WPUBT_B            0.061      0.018      3.348      0.001
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.125      0.041      3.088      0.002
##     WINTT_1            0.002      0.015      0.153      0.879
##     WPUBT_1            0.097      0.026      3.778      0.000
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.465      0.139      3.353      0.001
##     WINTT_2            0.018      0.015      1.194      0.232
##     WPUBT_2            0.056      0.036      1.547      0.122
## 
##  WPUBT_1  ON
##     WPUBT_B            0.345      0.029     11.838      0.000
##     WINTT_B            0.043      0.035      1.221      0.222
##     WWCHRT_B           0.070      0.109      0.641      0.521
## 
##  WPUBT_2  ON
##     WPUBT_1            0.422      0.028     15.131      0.000
##     WINTT_1           -0.022      0.015     -1.501      0.133
##     WWCHRT_1          -0.037      0.025     -1.456      0.145
## 
##  WPUBT_3  ON
##     WPUBT_2            0.354      0.028     12.758      0.000
##     WINTT_2            0.014      0.007      1.959      0.050
##     WWCHRT_2           0.028      0.025      1.084      0.278
## 
##  WINTT_1  ON
##     WINTT_B            0.027      0.085      0.319      0.750
##     WPUBT_B            0.107      0.043      2.510      0.012
##     WWCHRT_B           0.009      0.153      0.057      0.955
## 
##  WINTT_2  ON
##     WINTT_1            0.257      0.056      4.563      0.000
##     WPUBT_1            0.263      0.063      4.167      0.000
##     WWCHRT_1          -0.156      0.060     -2.618      0.009
## 
##  WINTT_3  ON
##     WINTT_2            0.504      0.038     13.433      0.000
##     WPUBT_2            0.203      0.050      4.054      0.000
##     WWCHRT_2           0.137      0.093      1.480      0.139
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.006      0.019      0.337      0.736
##     RI_WCHRT           0.128      0.021      5.942      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.071      0.008      8.666      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B            0.057      0.025      2.298      0.022
##     WWCHRT_B          -0.009      0.014     -0.663      0.507
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B            0.031      0.010      2.993      0.003
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1            0.097      0.031      3.119      0.002
##     WWCHRT_1          -0.020      0.022     -0.913      0.361
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.026      0.014      1.855      0.064
## 
##  WINTT_2  WITH
##     WPUBT_2            0.056      0.018      3.184      0.001
##     WWCHRT_2           0.016      0.015      1.065      0.287
## 
##  WPUBT_2  WITH
##     WWCHRT_2           0.003      0.006      0.438      0.661
## 
##  WINTT_3  WITH
##     WPUBT_3            0.063      0.016      4.040      0.000
##     WWCHRT_3           0.048      0.034      1.408      0.159
## 
##  WPUBT_3  WITH
##     WWCHRT_3           0.011      0.010      1.031      0.303
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.010      0.025      0.980
##     WCHRT_1            0.004      0.011      0.383      0.701
##     WCHRT_2            0.019      0.012      1.571      0.116
##     WCHRT_3           -0.084      0.020     -4.274      0.000
##     INTT_B             0.001      0.023      0.036      0.971
##     INTT_1             0.007      0.025      0.287      0.774
##     INTT_2             0.011      0.029      0.362      0.717
##     INTT_3             0.043      0.035      1.226      0.220
##     PUBT_B             0.002      0.014      0.125      0.901
##     PUBT_1             0.059      0.017      3.477      0.001
##     PUBT_2             0.010      0.012      0.901      0.367
##     PUBT_3             0.007      0.010      0.712      0.477
## 
##  Variances
##     RI_INTT            1.713      0.101     16.927      0.000
##     RI_PUBTT           0.118      0.016      7.492      0.000
##     RI_WCHRT           0.388      0.014     27.981      0.000
##     WINTT_B            0.927      0.088     10.504      0.000
##     WWCHRT_B           0.124      0.021      5.867      0.000
##     WPUBT_B            0.627      0.018     34.374      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.182      0.117     10.093      0.000
##     WINTT_2            2.104      0.122     17.294      0.000
##     WINTT_3            3.013      0.137     21.981      0.000
##     WWCHRT_1           0.223      0.042      5.334      0.000
##     WWCHRT_2           0.200      0.011     18.117      0.000
##     WWCHRT_3           0.273      0.055      4.952      0.000
##     WPUBT_1            0.498      0.019     25.563      0.000
##     WPUBT_2            0.353      0.012     30.130      0.000
##     WPUBT_3            0.257      0.011     22.376      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.801E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.806      0.017     48.056      0.000
##     INTT_1             0.768      0.021     36.569      0.000
##     INTT_2             0.658      0.016     41.947      0.000
##     INTT_3             0.566      0.015     37.839      0.000
## 
##  RI_PUBTT BY
##     PUBT_B             0.397      0.026     15.237      0.000
##     PUBT_1             0.411      0.029     14.232      0.000
##     PUBT_2             0.454      0.031     14.680      0.000
##     PUBT_3             0.521      0.035     15.046      0.000
## 
##  RI_WCHRT BY
##     WCHRT_B            0.871      0.019     45.088      0.000
##     WCHRT_1            0.795      0.028     28.328      0.000
##     WCHRT_2            0.806      0.009     88.532      0.000
##     WCHRT_3            0.739      0.039     19.056      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.593      0.023     26.008      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.640      0.025     25.420      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.753      0.014     54.944      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.825      0.010     80.351      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.492      0.034     14.365      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.607      0.037     16.521      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.593      0.012     47.907      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.674      0.043     15.847      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.918      0.011     81.327      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.912      0.013     70.071      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.891      0.016     56.677      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.854      0.021     40.444      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.036      0.058     -0.630      0.528
##     WINTT_B           -0.078      0.042     -1.850      0.064
##     WPUBT_B            0.102      0.033      3.073      0.002
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.130      0.040      3.263      0.001
##     WINTT_1            0.005      0.035      0.153      0.879
##     WPUBT_1            0.161      0.042      3.837      0.000
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.375      0.084      4.475      0.000
##     WINTT_2            0.047      0.042      1.133      0.257
##     WPUBT_2            0.066      0.042      1.569      0.117
## 
##  WPUBT_1  ON
##     WPUBT_B            0.359      0.028     12.872      0.000
##     WINTT_B            0.054      0.044      1.228      0.219
##     WWCHRT_B           0.032      0.050      0.643      0.520
## 
##  WPUBT_2  ON
##     WPUBT_1            0.477      0.029     16.552      0.000
##     WINTT_1           -0.036      0.024     -1.521      0.128
##     WWCHRT_1          -0.026      0.018     -1.462      0.144
## 
##  WPUBT_3  ON
##     WPUBT_2            0.424      0.030     14.294      0.000
##     WINTT_2            0.036      0.019      1.949      0.051
##     WWCHRT_2           0.022      0.021      1.076      0.282
## 
##  WINTT_1  ON
##     WINTT_B            0.024      0.075      0.320      0.749
##     WPUBT_B            0.078      0.031      2.499      0.012
##     WWCHRT_B           0.003      0.049      0.057      0.955
## 
##  WINTT_2  ON
##     WINTT_1            0.187      0.044      4.259      0.000
##     WPUBT_1            0.134      0.033      4.087      0.000
##     WWCHRT_1          -0.049      0.018     -2.698      0.007
## 
##  WINTT_3  ON
##     WINTT_2            0.396      0.028     14.306      0.000
##     WPUBT_2            0.072      0.018      4.092      0.000
##     WWCHRT_2           0.033      0.022      1.483      0.138
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.014      0.043      0.339      0.735
##     RI_WCHRT           0.157      0.025      6.268      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.331      0.038      8.641      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B            0.075      0.032      2.323      0.020
##     WWCHRT_B          -0.026      0.040     -0.660      0.509
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B            0.111      0.035      3.155      0.002
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1            0.126      0.041      3.094      0.002
##     WWCHRT_1          -0.040      0.044     -0.900      0.368
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.078      0.042      1.857      0.063
## 
##  WINTT_2  WITH
##     WPUBT_2            0.065      0.020      3.268      0.001
##     WWCHRT_2           0.024      0.023      1.071      0.284
## 
##  WPUBT_2  WITH
##     WWCHRT_2           0.010      0.022      0.438      0.661
## 
##  WINTT_3  WITH
##     WPUBT_3            0.072      0.018      4.058      0.000
##     WWCHRT_3           0.053      0.039      1.348      0.178
## 
##  WPUBT_3  WITH
##     WWCHRT_3           0.040      0.040      1.016      0.310
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.000      0.014      0.025      0.980
##     WCHRT_1            0.006      0.014      0.386      0.699
##     WCHRT_2            0.024      0.015      1.594      0.111
##     WCHRT_3           -0.099      0.025     -3.899      0.000
##     INTT_B             0.001      0.014      0.036      0.971
##     INTT_1             0.004      0.015      0.289      0.773
##     INTT_2             0.005      0.015      0.365      0.715
##     INTT_3             0.019      0.015      1.250      0.211
##     PUBT_B             0.002      0.016      0.125      0.901
##     PUBT_1             0.070      0.020      3.439      0.001
##     PUBT_2             0.014      0.015      0.897      0.370
##     PUBT_3             0.011      0.016      0.708      0.479
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     RI_PUBTT           1.000      0.000    999.000    999.000
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.993      0.006    155.392      0.000
##     WINTT_2            0.938      0.019     48.952      0.000
##     WINTT_3            0.828      0.023     36.709      0.000
##     WWCHRT_1           0.984      0.010    101.885      0.000
##     WWCHRT_2           0.953      0.019     51.456      0.000
##     WWCHRT_3           0.846      0.062     13.563      0.000
##     WPUBT_1            0.861      0.023     37.589      0.000
##     WPUBT_2            0.778      0.026     29.559      0.000
##     WPUBT_3            0.813      0.025     31.987      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.007      0.006      1.084      0.278
##     WINTT_2            0.062      0.019      3.236      0.001
##     WINTT_3            0.172      0.023      7.601      0.000
##     WWCHRT_1           0.016      0.010      1.619      0.105
##     WWCHRT_2           0.047      0.019      2.549      0.011
##     WWCHRT_3           0.154      0.062      2.463      0.014
##     WPUBT_1            0.139      0.023      6.044      0.000
##     WPUBT_2            0.222      0.026      8.416      0.000
##     WPUBT_3            0.187      0.025      7.376      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_INTT  BY INTT_B                35.388    -0.330     -0.432       -0.266
## RI_INTT  BY INTT_1                33.662     0.257      0.336        0.197
## RI_PUBTT BY PUBT_3                14.493    -0.460     -0.158       -0.240
## RI_WCHRT BY PUBT_3                16.809    -0.103     -0.064       -0.097
## WINTT_B  BY INTT_3                16.609    -0.187     -0.180       -0.078
## WINTT_1  BY INTT_2                37.330    -0.446     -0.486       -0.244
## WINTT_1  BY INTT_3                37.983     0.227      0.248        0.107
## WINTT_3  BY INTT_B                24.241    -0.075     -0.144       -0.088
## WINTT_3  BY INTT_1                36.756     0.083      0.159        0.093
## WINTT_3  BY INTT_2                32.328    -0.484     -0.924       -0.464
## WPUBT_B  BY PUBT_3                12.730    -0.092     -0.073       -0.110
## WPUBT_1  BY PUBT_2                16.209    -0.304     -0.231       -0.306
## WPUBT_1  BY PUBT_3                14.845     0.105      0.080        0.122
## WPUBT_3  BY PUBT_B                14.009    -0.224     -0.126       -0.146
## WPUBT_3  BY PUBT_1                18.720     0.163      0.092        0.110
## WPUBT_3  BY PUBT_2                16.726    -0.375     -0.211       -0.279
## 
## ON/BY Statements
## 
## RI_INTT  ON WINTT_B  /
## WINTT_B  BY RI_INTT               31.764    -0.590     -0.434       -0.434
## RI_INTT  ON WINTT_1  /
## WINTT_1  BY RI_INTT               37.863     0.453      0.378        0.378
## RI_PUBTT ON WPUBT_B  /
## WPUBT_B  BY RI_PUBTT              21.805    -0.331     -0.765       -0.765
## RI_PUBTT ON WPUBT_1  /
## WPUBT_1  BY RI_PUBTT              13.462     0.154      0.341        0.341
## RI_WCHRT ON WPUBT_B  /
## WPUBT_B  BY RI_WCHRT              10.372     0.079      0.100        0.100
## RI_WCHRT ON WPUBT_3  /
## WPUBT_3  BY RI_WCHRT              14.447    -0.187     -0.169       -0.169
## WINTT_B  ON RI_INTT  /
## RI_INTT  BY WINTT_B               35.625    -0.334     -0.455       -0.455
## WINTT_B  ON WINTT_3  /
## WINTT_3  BY WINTT_B               23.047    -0.074     -0.147       -0.147
## WINTT_1  ON RI_INTT  /
## RI_INTT  BY WINTT_1               36.215     0.309      0.370        0.370
## WINTT_1  ON WINTT_3  /
## WINTT_3  BY WINTT_1               36.743     0.087      0.151        0.151
## WINTT_2  ON WINTT_3  /
## WINTT_3  BY WINTT_2               32.329    -0.484     -0.617       -0.617
## WINTT_3  ON WINTT_B  /
## WINTT_B  BY WINTT_3               16.609    -0.187     -0.094       -0.094
## WINTT_3  ON WINTT_1  /
## WINTT_1  BY WINTT_3               37.983     0.227      0.130        0.130
## WPUBT_B  ON RI_WCHRT /
## RI_WCHRT BY WPUBT_B               11.141     0.133      0.105        0.105
## WPUBT_B  ON WWCHRT_3 /
## WWCHRT_3 BY WPUBT_B               10.932     0.236      0.169        0.169
## WPUBT_1  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_1               19.351     0.206      0.153        0.153
## WPUBT_2  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_2               16.724    -0.375     -0.313       -0.313
## WPUBT_3  ON RI_PUBTT /
## RI_PUBTT BY WPUBT_3               14.493    -0.460     -0.281       -0.281
## WPUBT_3  ON RI_WCHRT /
## RI_WCHRT BY WPUBT_3               16.809    -0.103     -0.114       -0.114
## WPUBT_3  ON WPUBT_B  /
## WPUBT_B  BY WPUBT_3               12.730    -0.092     -0.129       -0.129
## WPUBT_3  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_3               14.845     0.105      0.143        0.143
## 
## WITH Statements
## 
## WCHRT_3  WITH WCHRT_B             11.445    -0.040     -0.040      999.000
## INTT_2   WITH INTT_1              38.169    -0.507     -0.507      999.000
## INTT_3   WITH INTT_B              17.891    -0.178     -0.178      999.000
## INTT_3   WITH INTT_1              37.761     0.255      0.255      999.000
## INTT_3   WITH INTT_2              31.771    -1.445     -1.445      999.000
## PUBT_2   WITH PUBT_1              26.144    -0.111     -0.111      999.000
## PUBT_3   WITH PUBT_B              17.404    -0.051     -0.051      999.000
## PUBT_3   WITH PUBT_1              22.727     0.047      0.047      999.000
## PUBT_3   WITH PUBT_2              16.656    -0.096     -0.096      999.000
## WINTT_B  WITH RI_INTT             35.921    -0.585     -0.464       -0.464
## WINTT_1  WITH RI_INTT             36.663     0.520      0.365        0.365
## WINTT_3  WITH WINTT_B             16.893    -0.174     -0.104       -0.104
## WINTT_3  WITH WINTT_1             37.769     0.265      0.140        0.140
## WINTT_3  WITH WINTT_2             31.763    -1.445     -0.574       -0.574
## WWCHRT_3 WITH WWCHRT_B            11.609    -0.039     -0.210       -0.210
## WPUBT_B  WITH RI_PUBTT            21.174    -0.191     -0.705       -0.705
## WPUBT_B  WITH RI_WCHRT            10.944     0.051      0.103        0.103
## WPUBT_1  WITH RI_PUBTT            17.634     0.074      0.306        0.306
## WPUBT_3  WITH RI_WCHRT            13.915    -0.036     -0.113       -0.113
## WPUBT_3  WITH WPUBT_B             11.571    -0.053     -0.133       -0.133
## WPUBT_3  WITH WPUBT_1             24.324     0.060      0.169        0.169
## WPUBT_3  WITH WPUBT_2             16.654    -0.096     -0.320       -0.320
## 
## Variances/Residual Variances
## 
## INTT_2                            32.214     2.885      2.885        0.729
## PUBT_2                            16.330     0.263      0.263        0.461
## 
## 
## TECHNICAL 4 OUTPUT
## 
## 
##      ESTIMATES DERIVED FROM THE MODEL
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.713
##  RI_PUBTT       0.006         0.118
##  RI_WCHRT       0.128         0.071         0.388
##  WINTT_B        0.000         0.000         0.000         0.927
##  WINTT_1        0.000         0.000         0.000         0.031         1.191
##  WINTT_2        0.000         0.000         0.000         0.028         0.341
##  WINTT_3        0.000         0.000         0.000         0.020         0.179
##  WWCHRT_B       0.000         0.000         0.000        -0.009         0.004
##  WWCHRT_1       0.000         0.000         0.000        -0.032        -0.018
##  WWCHRT_2       0.000         0.000         0.000         0.002         0.012
##  WWCHRT_3       0.000         0.000         0.000         0.003         0.013
##  WPUBT_B        0.000         0.000         0.000         0.057         0.069
##  WPUBT_1        0.000         0.000         0.000         0.059         0.122
##  WPUBT_2        0.000         0.000         0.000         0.025         0.025
##  WPUBT_3        0.000         0.000         0.000         0.009         0.014
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        2.243
##  WINTT_3        1.160         3.637
##  WWCHRT_B       0.007         0.005         0.124
##  WWCHRT_1      -0.030        -0.009        -0.004         0.226
##  WWCHRT_2       0.030         0.049         0.001         0.032         0.210
##  WWCHRT_3       0.061         0.100         0.001         0.015         0.100
##  WPUBT_B        0.071         0.057         0.031         0.035         0.026
##  WPUBT_1        0.178         0.147         0.019         0.036         0.061
##  WPUBT_2        0.125         0.159         0.008         0.007         0.027
##  WPUBT_3        0.076         0.137         0.003         0.003         0.016
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.323
##  WPUBT_B        0.018         0.627
##  WPUBT_1        0.045         0.221         0.579
##  WPUBT_2        0.040         0.091         0.240         0.454
##  WPUBT_3        0.028         0.034         0.089         0.163         0.316
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.101
##  RI_PUBTT       0.019         0.016
##  RI_WCHRT       0.021         0.008         0.014
##  WINTT_B        0.000         0.000         0.000         0.088
##  WINTT_1        0.000         0.000         0.000         0.080         0.122
##  WINTT_2        0.000         0.000         0.000         0.026         0.088
##  WINTT_3        0.000         0.000         0.000         0.016         0.052
##  WWCHRT_B       0.000         0.000         0.000         0.014         0.019
##  WWCHRT_1       0.000         0.000         0.000         0.019         0.022
##  WWCHRT_2       0.000         0.000         0.000         0.005         0.020
##  WWCHRT_3       0.000         0.000         0.000         0.003         0.011
##  WPUBT_B        0.000         0.000         0.000         0.025         0.028
##  WPUBT_1        0.000         0.000         0.000         0.036         0.036
##  WPUBT_2        0.000         0.000         0.000         0.015         0.024
##  WPUBT_3        0.000         0.000         0.000         0.006         0.010
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.138
##  WINTT_3        0.119         0.187
##  WWCHRT_B       0.007         0.005         0.021
##  WWCHRT_1       0.017         0.010         0.009         0.041
##  WWCHRT_2       0.018         0.023         0.002         0.010         0.012
##  WWCHRT_3       0.034         0.040         0.002         0.007         0.029
##  WPUBT_B        0.020         0.014         0.010         0.011         0.007
##  WPUBT_1        0.042         0.029         0.016         0.016         0.017
##  WPUBT_2        0.025         0.030         0.007         0.009         0.010
##  WPUBT_3        0.020         0.023         0.003         0.004         0.007
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.073
##  WPUBT_B        0.007         0.018
##  WPUBT_1        0.015         0.023         0.027
##  WPUBT_2        0.018         0.014         0.023         0.022
##  WPUBT_3        0.013         0.007         0.014         0.018         0.020
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT       16.927
##  RI_PUBTT       0.337         7.492
##  RI_WCHRT       5.942         8.666        27.981
##  WINTT_B        0.000         0.000         0.000        10.504
##  WINTT_1        0.000         0.000         0.000         0.388         9.783
##  WINTT_2        0.000         0.000         0.000         1.104         3.859
##  WINTT_3        0.000         0.000         0.000         1.270         3.440
##  WWCHRT_B       0.000         0.000         0.000        -0.663         0.214
##  WWCHRT_1       0.000         0.000         0.000        -1.722        -0.795
##  WWCHRT_2       0.000         0.000         0.000         0.336         0.622
##  WWCHRT_3       0.000         0.000         0.000         0.784         1.154
##  WPUBT_B        0.000         0.000         0.000         2.298         2.422
##  WPUBT_1        0.000         0.000         0.000         1.624         3.363
##  WPUBT_2        0.000         0.000         0.000         1.638         1.063
##  WPUBT_3        0.000         0.000         0.000         1.590         1.443
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2       16.222
##  WINTT_3        9.758        19.456
##  WWCHRT_B       0.933         1.061         5.867
##  WWCHRT_1      -1.783        -0.908        -0.413         5.478
##  WWCHRT_2       1.640         2.137         0.562         3.277        17.173
##  WWCHRT_3       1.802         2.487         0.733         1.982         3.392
##  WPUBT_B        3.542         4.113         2.993         3.021         3.529
##  WPUBT_1        4.224         4.983         1.215         2.300         3.642
##  WPUBT_2        5.089         5.360         1.219         0.832         2.797
##  WPUBT_3        3.776         5.987         1.185         0.865         2.173
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       4.400
##  WPUBT_B        2.818        34.374
##  WPUBT_1        2.981         9.656        21.331
##  WPUBT_2        2.264         6.688        10.400        20.745
##  WPUBT_3        2.238         4.852         6.375         8.814        16.071
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.736         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.698         0.000
##  WINTT_2        1.000         1.000         1.000         0.269         0.000
##  WINTT_3        1.000         1.000         1.000         0.204         0.001
##  WWCHRT_B       1.000         1.000         1.000         0.507         0.831
##  WWCHRT_1       1.000         1.000         1.000         0.085         0.426
##  WWCHRT_2       1.000         1.000         1.000         0.737         0.534
##  WWCHRT_3       1.000         1.000         1.000         0.433         0.249
##  WPUBT_B        1.000         1.000         1.000         0.022         0.015
##  WPUBT_1        1.000         1.000         1.000         0.104         0.001
##  WPUBT_2        1.000         1.000         1.000         0.101         0.288
##  WPUBT_3        1.000         1.000         1.000         0.112         0.149
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.351         0.289         0.000
##  WWCHRT_1       0.075         0.364         0.680         0.000
##  WWCHRT_2       0.101         0.033         0.574         0.001         0.000
##  WWCHRT_3       0.072         0.013         0.463         0.048         0.001
##  WPUBT_B        0.000         0.000         0.003         0.003         0.000
##  WPUBT_1        0.000         0.000         0.224         0.021         0.000
##  WPUBT_2        0.000         0.000         0.223         0.405         0.005
##  WPUBT_3        0.000         0.000         0.236         0.387         0.030
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.005         0.000
##  WPUBT_1        0.003         0.000         0.000
##  WPUBT_2        0.024         0.000         0.000         0.000
##  WPUBT_3        0.025         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.000
##  RI_PUBTT       0.014         1.000
##  RI_WCHRT       0.157         0.331         1.000
##  WINTT_B        0.000         0.000         0.000         1.000
##  WINTT_1        0.000         0.000         0.000         0.030         1.000
##  WINTT_2        0.000         0.000         0.000         0.020         0.208
##  WINTT_3        0.000         0.000         0.000         0.011         0.086
##  WWCHRT_B       0.000         0.000         0.000        -0.026         0.011
##  WWCHRT_1       0.000         0.000         0.000        -0.070        -0.034
##  WWCHRT_2       0.000         0.000         0.000         0.004         0.025
##  WWCHRT_3       0.000         0.000         0.000         0.005         0.021
##  WPUBT_B        0.000         0.000         0.000         0.075         0.080
##  WPUBT_1        0.000         0.000         0.000         0.080         0.147
##  WPUBT_2        0.000         0.000         0.000         0.039         0.035
##  WPUBT_3        0.000         0.000         0.000         0.017         0.023
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.000
##  WINTT_3        0.406         1.000
##  WWCHRT_B       0.013         0.008         1.000
##  WWCHRT_1      -0.042        -0.010        -0.023         1.000
##  WWCHRT_2       0.044         0.057         0.008         0.146         1.000
##  WWCHRT_3       0.072         0.093         0.006         0.054         0.383
##  WPUBT_B        0.059         0.038         0.111         0.092         0.071
##  WPUBT_1        0.156         0.101         0.071         0.100         0.175
##  WPUBT_2        0.124         0.124         0.034         0.023         0.087
##  WPUBT_3        0.090         0.127         0.015         0.012         0.061
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       1.000
##  WPUBT_B        0.041         1.000
##  WPUBT_1        0.104         0.367         1.000
##  WPUBT_2        0.104         0.170         0.469         1.000
##  WPUBT_3        0.089         0.076         0.209         0.431         1.000
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.043         0.000
##  RI_WCHRT       0.025         0.038         0.000
##  WINTT_B        0.000         0.000         0.000         0.000
##  WINTT_1        0.000         0.000         0.000         0.074         0.000
##  WINTT_2        0.000         0.000         0.000         0.017         0.043
##  WINTT_3        0.000         0.000         0.000         0.008         0.021
##  WWCHRT_B       0.000         0.000         0.000         0.040         0.050
##  WWCHRT_1       0.000         0.000         0.000         0.041         0.043
##  WWCHRT_2       0.000         0.000         0.000         0.012         0.039
##  WWCHRT_3       0.000         0.000         0.000         0.006         0.018
##  WPUBT_B        0.000         0.000         0.000         0.032         0.032
##  WPUBT_1        0.000         0.000         0.000         0.049         0.042
##  WPUBT_2        0.000         0.000         0.000         0.024         0.032
##  WPUBT_3        0.000         0.000         0.000         0.011         0.016
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.028         0.000
##  WWCHRT_B       0.013         0.007         0.000
##  WWCHRT_1       0.023         0.011         0.058         0.000
##  WWCHRT_2       0.026         0.026         0.015         0.041         0.000
##  WWCHRT_3       0.042         0.042         0.008         0.023         0.083
##  WPUBT_B        0.016         0.009         0.035         0.032         0.019
##  WPUBT_1        0.036         0.019         0.057         0.043         0.046
##  WPUBT_2        0.023         0.022         0.027         0.028         0.030
##  WPUBT_3        0.023         0.021         0.012         0.013         0.027
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.013         0.000
##  WPUBT_1        0.030         0.029         0.000
##  WPUBT_2        0.044         0.021         0.028         0.000
##  WPUBT_3        0.039         0.013         0.024         0.030         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT      999.000
##  RI_PUBTT       0.339       999.000
##  RI_WCHRT       6.268         8.641       999.000
##  WINTT_B        0.000         0.000         0.000       999.000
##  WINTT_1        0.000         0.000         0.000         0.398       999.000
##  WINTT_2        0.000         0.000         0.000         1.138         4.834
##  WINTT_3        0.000         0.000         0.000         1.307         4.063
##  WWCHRT_B       0.000         0.000         0.000        -0.660         0.215
##  WWCHRT_1       0.000         0.000         0.000        -1.691        -0.789
##  WWCHRT_2       0.000         0.000         0.000         0.336         0.626
##  WWCHRT_3       0.000         0.000         0.000         0.785         1.155
##  WPUBT_B        0.000         0.000         0.000         2.323         2.494
##  WPUBT_1        0.000         0.000         0.000         1.631         3.462
##  WPUBT_2        0.000         0.000         0.000         1.642         1.070
##  WPUBT_3        0.000         0.000         0.000         1.602         1.466
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2      999.000
##  WINTT_3       14.698       999.000
##  WWCHRT_B       0.937         1.069       999.000
##  WWCHRT_1      -1.815        -0.914        -0.401       999.000
##  WWCHRT_2       1.657         2.161         0.571         3.573       999.000
##  WWCHRT_3       1.692         2.228         0.752         2.376         4.617
##  WPUBT_B        3.629         4.306         3.155         2.893         3.716
##  WPUBT_1        4.315         5.280         1.233         2.322         3.835
##  WPUBT_2        5.343         5.559         1.234         0.831         2.889
##  WPUBT_3        3.896         6.192         1.201         0.862         2.244
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3     999.000
##  WPUBT_B        3.240       999.000
##  WPUBT_1        3.438        12.714       999.000
##  WPUBT_2        2.388         8.219        16.783       999.000
##  WPUBT_3        2.304         5.762         8.627        14.588       999.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.735         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.691         0.000
##  WINTT_2        1.000         1.000         1.000         0.255         0.000
##  WINTT_3        1.000         1.000         1.000         0.191         0.000
##  WWCHRT_B       1.000         1.000         1.000         0.509         0.830
##  WWCHRT_1       1.000         1.000         1.000         0.091         0.430
##  WWCHRT_2       1.000         1.000         1.000         0.737         0.531
##  WWCHRT_3       1.000         1.000         1.000         0.432         0.248
##  WPUBT_B        1.000         1.000         1.000         0.020         0.013
##  WPUBT_1        1.000         1.000         1.000         0.103         0.001
##  WPUBT_2        1.000         1.000         1.000         0.101         0.284
##  WPUBT_3        1.000         1.000         1.000         0.109         0.143
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.349         0.285         0.000
##  WWCHRT_1       0.069         0.361         0.689         0.000
##  WWCHRT_2       0.098         0.031         0.568         0.000         0.000
##  WWCHRT_3       0.091         0.026         0.452         0.018         0.000
##  WPUBT_B        0.000         0.000         0.002         0.004         0.000
##  WPUBT_1        0.000         0.000         0.218         0.020         0.000
##  WPUBT_2        0.000         0.000         0.217         0.406         0.004
##  WPUBT_3        0.000         0.000         0.230         0.389         0.025
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.001         0.000
##  WPUBT_1        0.001         0.000         0.000
##  WPUBT_2        0.017         0.000         0.000         0.000
##  WPUBT_3        0.021         0.000         0.000         0.000         0.000
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\all full model girls.dgm
## 
##      Beginning Time:  14:24:53
##         Ending Time:  14:24:53
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

Black Youth Model (No Covariates)

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/black full model.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/02/2024  11:58 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Full Sample Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3
##   intt_b intt_1
##   intt_2 intt_3
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   USEOBSERVATIONS ARE (race3 EQ 2);
## 
##   DEFINE:
##   wchrt_b = wchrt_b*10;
##   wchrt_1 = wchrt_1*10;
##   wchrt_2 = wchrt_2*10;
##   wchrt_3 = wchrt_3*10;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
##   COVERAGE = 0;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
##   RI_pubtT BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! RI correlations
##   RI_intt with RI_pubtT RI_wchrt;
##   RI_pubtT with RI_wchrt;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b;
##   wwchrt_1 ON wintt_b;
##   wwchrt_1 ON wpubt_b;
## 
##   wwchrt_2 ON wwchrt_1;
##   wwchrt_2 ON wintt_1;
##   wwchrt_2 ON wpubt_1;
## 
##   wwchrt_3 ON wwchrt_2;
##   wwchrt_3 ON wintt_2;
##   wwchrt_3 ON wpubt_2;
## 
##   wpubt_1 ON wpubt_b;
##   wpubt_1 ON wintt_b;
##   wpubt_1 ON wwchrt_b;
## 
##   wpubt_2 ON wpubt_1;
##   wpubt_2 ON wintt_1;
##   wpubt_2 ON wwchrt_1;
## 
##   wpubt_3 ON wpubt_2;
##   wpubt_3 ON wintt_2;
##   wpubt_3 ON wwchrt_2;
## 
##   wintt_1 ON wintt_b;
##   wintt_1 ON wpubt_b;
##   wintt_1 ON wwchrt_b;
## 
##   wintt_2 ON wintt_1;
##   wintt_2 ON wpubt_1;
##   wintt_2 ON wwchrt_1;
## 
##   wintt_3 ON wintt_2;
##   wintt_3 ON wpubt_2;
##   wintt_3 ON wwchrt_2;
## 
##   ! Estimate the covariance between the within-person
##   ! centered variables at the first wave
##   wintt_b with wpubt_b;
##   wwchrt_b with wintt_b wpubt_b;
## 
##   ! Estimate covariances between residuals of within-person components
##   ! (i.e., innovations)
##   wintt_1 with wpubt_1 wwchrt_1;
##   wpubt_1 with wwchrt_1;
## 
##   wintt_2 with wpubt_2 wwchrt_2;
##   wpubt_2 with wwchrt_2;
## 
##   wintt_3 with wpubt_3 wwchrt_3;
##   wpubt_3 with wwchrt_3;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
##   [pubt_b pubt_1 pubt_2 pubt_3];
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_intt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_pubtT with wwchrt_b@0 wintt_b@0 wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES Tech4;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  2
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Full Sample Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                        1782
## 
## Number of dependent variables                                   12
## Number of independent variables                                  0
## Number of continuous latent variables                           15
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3     INTT_B      INTT_1
##    INTT_2      INTT_3      PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_INTT     RI_PUBTT    RI_WCHRT    WINTT_B     WINTT_1     WINTT_2
##    WINTT_3     WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3    WPUBT_B
##    WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns           125
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.000
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3       INTT_B
##               ________      ________      ________      ________      ________
##  WCHRT_B        0.999
##  WCHRT_1        0.878         0.879
##  WCHRT_2        0.668         0.632         0.669
##  WCHRT_3        0.148         0.144         0.125         0.148
##  INTT_B         0.999         0.878         0.669         0.148         0.999
##  INTT_1         0.893         0.878         0.640         0.145         0.893
##  INTT_2         0.868         0.809         0.668         0.143         0.868
##  INTT_3         0.744         0.701         0.572         0.148         0.744
##  PUBT_B         0.791         0.693         0.531         0.126         0.791
##  PUBT_1         0.276         0.272         0.266         0.061         0.276
##  PUBT_2         0.796         0.744         0.614         0.130         0.797
##  PUBT_3         0.694         0.654         0.536         0.135         0.695
## 
## 
##            Covariance Coverage
##               INTT_1        INTT_2        INTT_3        PUBT_B        PUBT_1
##               ________      ________      ________      ________      ________
##  INTT_1         0.893
##  INTT_2         0.824         0.868
##  INTT_3         0.715         0.720         0.744
##  PUBT_B         0.705         0.685         0.586         0.791
##  PUBT_1         0.276         0.270         0.250         0.239         0.276
##  PUBT_2         0.756         0.791         0.662         0.636         0.258
##  PUBT_3         0.667         0.672         0.680         0.551         0.241
## 
## 
##            Covariance Coverage
##               PUBT_2        PUBT_3
##               ________      ________
##  PUBT_2         0.797
##  PUBT_3         0.633         0.695
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B               0.119       0.824      -2.057    0.06%      -0.558     -0.224     -0.041
##             1780.000       0.645       0.648       4.101    0.06%       0.171      0.768
##      WCHRT_1               0.145       0.978      -1.763    0.06%      -0.569     -0.243     -0.044
##             1566.000       0.685       1.406       5.188    0.06%       0.211      0.817
##      WCHRT_2               0.229       1.783      -1.811    0.08%      -0.544     -0.188      0.012
##             1192.000       0.907       8.590       9.219    0.08%       0.288      0.939
##      WCHRT_3               0.284       0.859      -1.221    0.38%      -0.648     -0.207      0.067
##              264.000       1.001       0.649       4.586    0.38%       0.357      1.156
##      INTT_B                0.057       2.502      -1.161    0.45%      -1.092     -0.929     -0.912
##             1781.000       3.287       7.339      10.864    0.06%      -0.125      0.922
##      INTT_1                0.012       2.546      -1.298    0.06%      -1.122     -1.038     -0.993
##             1592.000       3.263       8.416      12.777    0.06%      -0.139      0.912
##      INTT_2               -0.094       2.667      -1.639    0.13%      -1.281     -1.133     -1.043
##             1547.000       3.590       9.684      13.660    0.06%      -0.340      0.803
##      INTT_3               -0.187       2.287      -1.781    0.08%      -1.470     -1.339     -1.263
##             1326.000       4.272       6.001      12.465    0.08%      -0.507      0.643
##      PUBT_B                0.321      -0.112      -1.577    0.07%      -0.322      0.067      0.437
##             1410.000       0.654      -0.149       3.081    0.07%       0.650      1.047
##      PUBT_1                0.361      -0.305      -2.004    0.20%      -0.069      0.142      0.274
##              491.000       0.560       0.214       2.473    0.20%       0.592      1.035
##      PUBT_2                0.278      -0.372      -2.227    0.07%      -0.304      0.142      0.369
##             1420.000       0.560       0.531       2.822    0.07%       0.531      0.887
##      PUBT_3                0.179      -0.531      -2.858    0.08%      -0.390      0.115      0.230
##             1238.000       0.495       1.235       2.306    0.08%       0.362      0.637
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       69
## 
## Loglikelihood
## 
##           H0 Value                      -21047.189
##           H0 Scaling Correction Factor      1.9353
##             for MLR
##           H1 Value                      -21025.684
##           H1 Scaling Correction Factor      1.7309
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                   42232.378
##           Bayesian (BIC)                 42610.877
##           Sample-Size Adjusted BIC       42391.669
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                             40.604*
##           Degrees of Freedom                    21
##           P-Value                           0.0063
##           Scaling Correction Factor         1.0593
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.023
##           90 Percent C.I.                    0.012  0.033
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.995
##           TLI                                0.983
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           3663.489
##           Degrees of Freedom                    66
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.024
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  RI_PUBTT BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.155      0.238     -0.652      0.515
##     WINTT_B           -0.056      0.029     -1.889      0.059
##     WPUBT_B            0.036      0.034      1.034      0.301
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.386      0.071      5.420      0.000
##     WINTT_1           -0.021      0.027     -0.780      0.436
##     WPUBT_1           -0.016      0.054     -0.293      0.769
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.425      0.151      2.815      0.005
##     WINTT_2           -0.038      0.023     -1.621      0.105
##     WPUBT_2           -0.145      0.058     -2.508      0.012
## 
##  WPUBT_1  ON
##     WPUBT_B            0.137      0.065      2.104      0.035
##     WINTT_B           -0.044      0.041     -1.069      0.285
##     WWCHRT_B           0.011      0.253      0.044      0.965
## 
##  WPUBT_2  ON
##     WPUBT_1            0.231      0.066      3.505      0.000
##     WINTT_1            0.002      0.026      0.065      0.948
##     WWCHRT_1          -0.118      0.081     -1.453      0.146
## 
##  WPUBT_3  ON
##     WPUBT_2            0.190      0.050      3.809      0.000
##     WINTT_2           -0.021      0.019     -1.074      0.283
##     WWCHRT_2          -0.028      0.048     -0.575      0.566
## 
##  WINTT_1  ON
##     WINTT_B            0.261      0.080      3.255      0.001
##     WPUBT_B            0.067      0.070      0.949      0.343
##     WWCHRT_B          -0.407      0.330     -1.232      0.218
## 
##  WINTT_2  ON
##     WINTT_1            0.262      0.091      2.882      0.004
##     WPUBT_1            0.007      0.139      0.052      0.959
##     WWCHRT_1          -0.116      0.143     -0.812      0.417
## 
##  WINTT_3  ON
##     WINTT_2            0.450      0.074      6.052      0.000
##     WPUBT_2            0.035      0.089      0.394      0.694
##     WWCHRT_2           0.175      0.125      1.405      0.160
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.028      0.029      0.945      0.345
##     RI_WCHRT           0.082      0.041      2.008      0.045
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.036      0.013      2.769      0.006
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B           -0.007      0.038     -0.188      0.850
##     WWCHRT_B          -0.067      0.037     -1.825      0.068
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B            0.002      0.016      0.108      0.914
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1           -0.021      0.052     -0.403      0.687
##     WWCHRT_1          -0.041      0.040     -1.029      0.303
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.002      0.029      0.071      0.943
## 
##  WINTT_2  WITH
##     WPUBT_2            0.025      0.033      0.749      0.454
##     WWCHRT_2          -0.001      0.032     -0.039      0.969
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.033      0.015     -2.288      0.022
## 
##  WINTT_3  WITH
##     WPUBT_3            0.023      0.033      0.680      0.496
##     WWCHRT_3           0.065      0.060      1.090      0.276
## 
##  WPUBT_3  WITH
##     WWCHRT_3           0.003      0.021      0.149      0.882
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.119      0.019      6.268      0.000
##     WCHRT_1            0.144      0.020      7.252      0.000
##     WCHRT_2            0.242      0.025      9.746      0.000
##     WCHRT_3            0.135      0.036      3.799      0.000
##     INTT_B             0.057      0.043      1.323      0.186
##     INTT_1             0.015      0.044      0.338      0.735
##     INTT_2            -0.078      0.048     -1.644      0.100
##     INTT_3            -0.165      0.055     -3.018      0.003
##     PUBT_B             0.321      0.021     15.004      0.000
##     PUBT_1             0.358      0.031     11.401      0.000
##     PUBT_2             0.280      0.020     14.305      0.000
##     PUBT_3             0.171      0.020      8.611      0.000
## 
##  Variances
##     RI_INTT            1.690      0.186      9.094      0.000
##     RI_PUBTT           0.116      0.019      6.080      0.000
##     RI_WCHRT           0.549      0.030     18.589      0.000
##     WINTT_B            1.641      0.199      8.238      0.000
##     WWCHRT_B           0.099      0.024      4.093      0.000
##     WPUBT_B            0.538      0.027     19.719      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.368      0.159      8.580      0.000
##     WINTT_2            1.861      0.217      8.557      0.000
##     WINTT_3            2.190      0.189     11.589      0.000
##     WWCHRT_1           0.114      0.030      3.763      0.000
##     WWCHRT_2           0.333      0.076      4.402      0.000
##     WWCHRT_3           0.237      0.034      6.952      0.000
##     WPUBT_1            0.439      0.037     11.755      0.000
##     WPUBT_2            0.410      0.024     17.299      0.000
##     WPUBT_3            0.369      0.024     15.638      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.216E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.712      0.031     22.713      0.000
##     INTT_1             0.726      0.035     20.468      0.000
##     INTT_2             0.680      0.034     20.054      0.000
##     INTT_3             0.628      0.031     20.497      0.000
## 
##  RI_PUBTT BY
##     PUBT_B             0.421      0.034     12.399      0.000
##     PUBT_1             0.451      0.040     11.300      0.000
##     PUBT_2             0.458      0.038     12.041      0.000
##     PUBT_3             0.480      0.038     12.637      0.000
## 
##  RI_WCHRT BY
##     WCHRT_B            0.921      0.020     47.178      0.000
##     WCHRT_1            0.905      0.019     47.031      0.000
##     WCHRT_2            0.780      0.035     22.459      0.000
##     WCHRT_3            0.795      0.018     44.590      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.702      0.032     22.055      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.687      0.038     18.319      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.734      0.031     23.377      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.778      0.025     31.490      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.390      0.046      8.481      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.425      0.041     10.367      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.625      0.043     14.434      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.606      0.023     25.892      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.907      0.016     57.719      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.893      0.020     44.265      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.889      0.020     45.425      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.877      0.021     42.228      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.140      0.212     -0.659      0.510
##     WINTT_B           -0.205      0.111     -1.846      0.065
##     WPUBT_B            0.075      0.073      1.032      0.302
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.226      0.059      3.856      0.000
##     WINTT_1           -0.044      0.054     -0.817      0.414
##     WPUBT_1           -0.018      0.061     -0.295      0.768
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.447      0.143      3.116      0.002
##     WINTT_2           -0.093      0.056     -1.656      0.098
##     WPUBT_2           -0.169      0.067     -2.529      0.011
## 
##  WPUBT_1  ON
##     WPUBT_B            0.149      0.069      2.159      0.031
##     WINTT_B           -0.084      0.077     -1.089      0.276
##     WWCHRT_B           0.005      0.118      0.044      0.965
## 
##  WPUBT_2  ON
##     WPUBT_1            0.235      0.068      3.472      0.001
##     WINTT_1            0.003      0.049      0.065      0.948
##     WWCHRT_1          -0.062      0.041     -1.500      0.134
## 
##  WPUBT_3  ON
##     WPUBT_2            0.202      0.053      3.805      0.000
##     WINTT_2           -0.047      0.043     -1.087      0.277
##     WWCHRT_2          -0.027      0.046     -0.576      0.565
## 
##  WINTT_1  ON
##     WINTT_B            0.272      0.077      3.537      0.000
##     WPUBT_B            0.040      0.042      0.943      0.346
##     WWCHRT_B          -0.104      0.084     -1.244      0.214
## 
##  WINTT_2  ON
##     WINTT_1            0.230      0.079      2.916      0.004
##     WPUBT_1            0.003      0.067      0.052      0.959
##     WWCHRT_1          -0.029      0.036     -0.802      0.423
## 
##  WINTT_3  ON
##     WINTT_2            0.392      0.069      5.689      0.000
##     WPUBT_2            0.014      0.037      0.395      0.693
##     WWCHRT_2           0.065      0.045      1.433      0.152
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.063      0.067      0.931      0.352
##     RI_WCHRT           0.085      0.042      2.017      0.044
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.145      0.054      2.693      0.007
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B           -0.008      0.040     -0.189      0.850
##     WWCHRT_B          -0.167      0.093     -1.795      0.073
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B            0.007      0.069      0.108      0.914
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1           -0.027      0.067     -0.403      0.687
##     WWCHRT_1          -0.103      0.104     -0.993      0.321
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.009      0.128      0.071      0.943
## 
##  WINTT_2  WITH
##     WPUBT_2            0.028      0.038      0.746      0.456
##     WWCHRT_2          -0.002      0.040     -0.039      0.969
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.090      0.034     -2.698      0.007
## 
##  WINTT_3  WITH
##     WPUBT_3            0.025      0.037      0.680      0.496
##     WWCHRT_3           0.090      0.080      1.124      0.261
## 
##  WPUBT_3  WITH
##     WWCHRT_3           0.011      0.071      0.148      0.882
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B            0.148      0.022      6.641      0.000
##     WCHRT_1            0.176      0.023      7.814      0.000
##     WCHRT_2            0.255      0.022     11.555      0.000
##     WCHRT_3            0.145      0.037      3.888      0.000
##     INTT_B             0.031      0.023      1.377      0.169
##     INTT_1             0.008      0.024      0.341      0.733
##     INTT_2            -0.041      0.026     -1.559      0.119
##     INTT_3            -0.079      0.029     -2.775      0.006
##     PUBT_B             0.397      0.028     14.215      0.000
##     PUBT_1             0.475      0.048      9.892      0.000
##     PUBT_2             0.377      0.029     12.946      0.000
##     PUBT_3             0.242      0.031      7.932      0.000
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     RI_PUBTT           1.000      0.000    999.000    999.000
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.904      0.044     20.398      0.000
##     WINTT_2            0.945      0.037     25.666      0.000
##     WINTT_3            0.843      0.053     15.993      0.000
##     WWCHRT_1           0.942      0.072     13.135      0.000
##     WWCHRT_2           0.945      0.025     37.245      0.000
##     WWCHRT_3           0.744      0.127      5.850      0.000
##     WPUBT_1            0.970      0.024     39.773      0.000
##     WPUBT_2            0.942      0.032     29.554      0.000
##     WPUBT_3            0.956      0.022     44.143      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.096      0.044      2.158      0.031
##     WINTT_2            0.055      0.037      1.503      0.133
##     WINTT_3            0.157      0.053      2.970      0.003
##     WWCHRT_1           0.058      0.072      0.803      0.422
##     WWCHRT_2           0.055      0.025      2.188      0.029
##     WWCHRT_3           0.256      0.127      2.009      0.045
##     WPUBT_1            0.030      0.024      1.213      0.225
##     WPUBT_2            0.058      0.032      1.823      0.068
##     WPUBT_3            0.044      0.022      2.038      0.042
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## WITH Statements
## 
## PUBT_2   WITH PUBT_1              11.930    -0.291     -0.291      999.000
## 
## 
## TECHNICAL 4 OUTPUT
## 
## 
##      ESTIMATES DERIVED FROM THE MODEL
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.690
##  RI_PUBTT       0.028         0.116
##  RI_WCHRT       0.082         0.036         0.549
##  WINTT_B        0.000         0.000         0.000         1.641
##  WINTT_1        0.000         0.000         0.000         0.456         1.513
##  WINTT_2        0.000         0.000         0.000         0.128         0.403
##  WINTT_3        0.000         0.000         0.000         0.051         0.172
##  WWCHRT_B       0.000         0.000         0.000        -0.067        -0.058
##  WWCHRT_1       0.000         0.000         0.000        -0.081        -0.056
##  WWCHRT_2       0.000         0.000         0.000        -0.040        -0.053
##  WWCHRT_3       0.000         0.000         0.000        -0.021        -0.038
##  WPUBT_B        0.000         0.000         0.000        -0.007         0.033
##  WPUBT_1        0.000         0.000         0.000        -0.074        -0.037
##  WPUBT_2        0.000         0.000         0.000        -0.007         0.001
##  WPUBT_3        0.000         0.000         0.000        -0.003        -0.007
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.970
##  WINTT_3        0.883         2.596
##  WWCHRT_B      -0.014        -0.007         0.099
##  WWCHRT_1      -0.029        -0.005        -0.011         0.121
##  WWCHRT_2      -0.021         0.051        -0.003         0.048         0.353
##  WWCHRT_3      -0.087         0.051        -0.001         0.023         0.157
##  WPUBT_B        0.007         0.005         0.002         0.019         0.006
##  WPUBT_1       -0.007         0.000         0.004         0.008        -0.003
##  WPUBT_2        0.027         0.020         0.002        -0.012        -0.040
##  WPUBT_3       -0.035         0.007         0.001        -0.003        -0.017
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.319
##  WPUBT_B        0.000         0.538
##  WPUBT_1       -0.016         0.074         0.453
##  WPUBT_2       -0.081         0.015         0.103         0.436
##  WPUBT_3       -0.015         0.003         0.020         0.083         0.386
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.186
##  RI_PUBTT       0.029         0.019
##  RI_WCHRT       0.041         0.013         0.030
##  WINTT_B        0.000         0.000         0.000         0.199
##  WINTT_1        0.000         0.000         0.000         0.162         0.222
##  WINTT_2        0.000         0.000         0.000         0.073         0.176
##  WINTT_3        0.000         0.000         0.000         0.037         0.097
##  WWCHRT_B       0.000         0.000         0.000         0.037         0.038
##  WWCHRT_1       0.000         0.000         0.000         0.039         0.043
##  WWCHRT_2       0.000         0.000         0.000         0.023         0.052
##  WWCHRT_3       0.000         0.000         0.000         0.013         0.025
##  WPUBT_B        0.000         0.000         0.000         0.038         0.043
##  WPUBT_1        0.000         0.000         0.000         0.065         0.063
##  WPUBT_2        0.000         0.000         0.000         0.023         0.044
##  WPUBT_3        0.000         0.000         0.000         0.006         0.013
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.270
##  WINTT_3        0.234         0.273
##  WWCHRT_B       0.013         0.006         0.024
##  WWCHRT_1       0.024         0.014         0.020         0.025
##  WWCHRT_2       0.042         0.048         0.008         0.015         0.077
##  WWCHRT_3       0.049         0.070         0.004         0.010         0.059
##  WPUBT_B        0.018         0.008         0.016         0.017         0.009
##  WPUBT_1        0.072         0.035         0.025         0.026         0.031
##  WPUBT_2        0.042         0.049         0.007         0.011         0.018
##  WPUBT_3        0.040         0.041         0.001         0.003         0.018
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.036
##  WPUBT_B        0.005         0.027
##  WPUBT_1        0.016         0.036         0.042
##  WPUBT_2        0.026         0.012         0.034         0.028
##  WPUBT_3        0.022         0.003         0.010         0.025         0.027
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        9.094
##  RI_PUBTT       0.945         6.080
##  RI_WCHRT       2.008         2.769        18.589
##  WINTT_B        0.000         0.000         0.000         8.238
##  WINTT_1        0.000         0.000         0.000         2.811         6.817
##  WINTT_2        0.000         0.000         0.000         1.770         2.295
##  WINTT_3        0.000         0.000         0.000         1.353         1.768
##  WWCHRT_B       0.000         0.000         0.000        -1.825        -1.527
##  WWCHRT_1       0.000         0.000         0.000        -2.064        -1.305
##  WWCHRT_2       0.000         0.000         0.000        -1.717        -1.019
##  WWCHRT_3       0.000         0.000         0.000        -1.643        -1.502
##  WPUBT_B        0.000         0.000         0.000        -0.188         0.770
##  WPUBT_1        0.000         0.000         0.000        -1.141        -0.587
##  WPUBT_2        0.000         0.000         0.000        -0.300         0.015
##  WPUBT_3        0.000         0.000         0.000        -0.473        -0.533
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        7.296
##  WINTT_3        3.781         9.518
##  WWCHRT_B      -1.049        -1.139         4.093
##  WWCHRT_1      -1.208        -0.357        -0.578         4.827
##  WWCHRT_2      -0.496         1.077        -0.388         3.255         4.574
##  WWCHRT_3      -1.772         0.722        -0.274         2.221         2.653
##  WPUBT_B        0.387         0.559         0.108         1.151         0.614
##  WPUBT_1       -0.102        -0.007         0.172         0.307        -0.106
##  WPUBT_2        0.645         0.422         0.328        -1.092        -2.185
##  WPUBT_3       -0.884         0.164         0.553        -0.910        -0.954
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       8.739
##  WPUBT_B       -0.009        19.719
##  WPUBT_1       -0.992         2.023        10.658
##  WPUBT_2       -3.063         1.267         3.053        15.361
##  WPUBT_3       -0.667         0.921         2.001         3.366        14.123
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.345         0.000
##  RI_WCHRT       0.045         0.006         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.005         0.000
##  WINTT_2        1.000         1.000         1.000         0.077         0.022
##  WINTT_3        1.000         1.000         1.000         0.176         0.077
##  WWCHRT_B       1.000         1.000         1.000         0.068         0.127
##  WWCHRT_1       1.000         1.000         1.000         0.039         0.192
##  WWCHRT_2       1.000         1.000         1.000         0.086         0.308
##  WWCHRT_3       1.000         1.000         1.000         0.100         0.133
##  WPUBT_B        1.000         1.000         1.000         0.850         0.441
##  WPUBT_1        1.000         1.000         1.000         0.254         0.557
##  WPUBT_2        1.000         1.000         1.000         0.764         0.988
##  WPUBT_3        1.000         1.000         1.000         0.636         0.594
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.294         0.255         0.000
##  WWCHRT_1       0.227         0.721         0.563         0.000
##  WWCHRT_2       0.620         0.281         0.698         0.001         0.000
##  WWCHRT_3       0.076         0.471         0.784         0.026         0.008
##  WPUBT_B        0.698         0.576         0.914         0.250         0.539
##  WPUBT_1        0.918         0.994         0.864         0.758         0.915
##  WPUBT_2        0.519         0.673         0.743         0.275         0.029
##  WPUBT_3        0.377         0.870         0.581         0.363         0.340
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.992         0.000
##  WPUBT_1        0.321         0.043         0.000
##  WPUBT_2        0.002         0.205         0.002         0.000
##  WPUBT_3        0.505         0.357         0.045         0.001         0.000
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.000
##  RI_PUBTT       0.063         1.000
##  RI_WCHRT       0.085         0.145         1.000
##  WINTT_B        0.000         0.000         0.000         1.000
##  WINTT_1        0.000         0.000         0.000         0.289         1.000
##  WINTT_2        0.000         0.000         0.000         0.071         0.233
##  WINTT_3        0.000         0.000         0.000         0.024         0.087
##  WWCHRT_B       0.000         0.000         0.000        -0.167        -0.149
##  WWCHRT_1       0.000         0.000         0.000        -0.182        -0.131
##  WWCHRT_2       0.000         0.000         0.000        -0.052        -0.073
##  WWCHRT_3       0.000         0.000         0.000        -0.029        -0.054
##  WPUBT_B        0.000         0.000         0.000        -0.008         0.037
##  WPUBT_1        0.000         0.000         0.000        -0.086        -0.045
##  WPUBT_2        0.000         0.000         0.000        -0.008         0.001
##  WPUBT_3        0.000         0.000         0.000        -0.004        -0.009
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.000
##  WINTT_3        0.390         1.000
##  WWCHRT_B      -0.031        -0.013         1.000
##  WWCHRT_1      -0.059        -0.009        -0.105         1.000
##  WWCHRT_2      -0.025         0.054        -0.018         0.231         1.000
##  WWCHRT_3      -0.109         0.056        -0.007         0.118         0.467
##  WPUBT_B        0.007         0.004         0.007         0.075         0.013
##  WPUBT_1       -0.008         0.000         0.020         0.035        -0.008
##  WPUBT_2        0.029         0.019         0.011        -0.054        -0.102
##  WPUBT_3       -0.040         0.007         0.004        -0.014        -0.046
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       1.000
##  WPUBT_B        0.000         1.000
##  WPUBT_1       -0.042         0.149         1.000
##  WPUBT_2       -0.217         0.031         0.233         1.000
##  WPUBT_3       -0.042         0.006         0.048         0.203         1.000
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.067         0.000
##  RI_WCHRT       0.042         0.054         0.000
##  WINTT_B        0.000         0.000         0.000         0.000
##  WINTT_1        0.000         0.000         0.000         0.074         0.000
##  WINTT_2        0.000         0.000         0.000         0.036         0.079
##  WINTT_3        0.000         0.000         0.000         0.017         0.043
##  WWCHRT_B       0.000         0.000         0.000         0.093         0.095
##  WWCHRT_1       0.000         0.000         0.000         0.087         0.098
##  WWCHRT_2       0.000         0.000         0.000         0.028         0.067
##  WWCHRT_3       0.000         0.000         0.000         0.017         0.035
##  WPUBT_B        0.000         0.000         0.000         0.040         0.048
##  WPUBT_1        0.000         0.000         0.000         0.075         0.076
##  WPUBT_2        0.000         0.000         0.000         0.027         0.054
##  WPUBT_3        0.000         0.000         0.000         0.008         0.016
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.068         0.000
##  WWCHRT_B       0.028         0.011         0.000
##  WWCHRT_1       0.046         0.025         0.201         0.000
##  WWCHRT_2       0.048         0.051         0.048         0.056         0.000
##  WWCHRT_3       0.060         0.077         0.025         0.043         0.144
##  WPUBT_B        0.018         0.007         0.069         0.066         0.021
##  WPUBT_1        0.076         0.032         0.118         0.113         0.077
##  WPUBT_2        0.045         0.046         0.033         0.049         0.040
##  WPUBT_3        0.045         0.041         0.008         0.015         0.048
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.012         0.000
##  WPUBT_1        0.042         0.069         0.000
##  WPUBT_2        0.068         0.023         0.067         0.000
##  WPUBT_3        0.063         0.006         0.022         0.053         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT      999.000
##  RI_PUBTT       0.931       999.000
##  RI_WCHRT       2.017         2.693       999.000
##  WINTT_B        0.000         0.000         0.000       999.000
##  WINTT_1        0.000         0.000         0.000         3.910       999.000
##  WINTT_2        0.000         0.000         0.000         2.004         2.948
##  WINTT_3        0.000         0.000         0.000         1.448         2.033
##  WWCHRT_B       0.000         0.000         0.000        -1.795        -1.575
##  WWCHRT_1       0.000         0.000         0.000        -2.080        -1.338
##  WWCHRT_2       0.000         0.000         0.000        -1.884        -1.086
##  WWCHRT_3       0.000         0.000         0.000        -1.725        -1.559
##  WPUBT_B        0.000         0.000         0.000        -0.189         0.764
##  WPUBT_1        0.000         0.000         0.000        -1.147        -0.592
##  WPUBT_2        0.000         0.000         0.000        -0.300         0.015
##  WPUBT_3        0.000         0.000         0.000        -0.475        -0.538
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2      999.000
##  WINTT_3        5.723       999.000
##  WWCHRT_B      -1.114        -1.163       999.000
##  WWCHRT_1      -1.273        -0.360        -0.522       999.000
##  WWCHRT_2      -0.513         1.049        -0.370         4.115       999.000
##  WWCHRT_3      -1.808         0.719        -0.267         2.718         3.240
##  WPUBT_B        0.389         0.560         0.108         1.151         0.602
##  WPUBT_1       -0.102        -0.007         0.172         0.308        -0.106
##  WPUBT_2        0.642         0.421         0.324        -1.096        -2.515
##  WPUBT_3       -0.884         0.164         0.539        -0.929        -0.965
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3     999.000
##  WPUBT_B       -0.009       999.000
##  WPUBT_1       -1.012         2.171       999.000
##  WPUBT_2       -3.206         1.315         3.488       999.000
##  WPUBT_3       -0.668         0.943         2.168         3.859       999.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.352         0.000
##  RI_WCHRT       0.044         0.007         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.000         0.000
##  WINTT_2        1.000         1.000         1.000         0.045         0.003
##  WINTT_3        1.000         1.000         1.000         0.148         0.042
##  WWCHRT_B       1.000         1.000         1.000         0.073         0.115
##  WWCHRT_1       1.000         1.000         1.000         0.037         0.181
##  WWCHRT_2       1.000         1.000         1.000         0.060         0.277
##  WWCHRT_3       1.000         1.000         1.000         0.084         0.119
##  WPUBT_B        1.000         1.000         1.000         0.850         0.445
##  WPUBT_1        1.000         1.000         1.000         0.251         0.554
##  WPUBT_2        1.000         1.000         1.000         0.764         0.988
##  WPUBT_3        1.000         1.000         1.000         0.635         0.590
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.265         0.245         0.000
##  WWCHRT_1       0.203         0.719         0.602         0.000
##  WWCHRT_2       0.608         0.294         0.712         0.000         0.000
##  WWCHRT_3       0.071         0.472         0.789         0.007         0.001
##  WPUBT_B        0.697         0.576         0.914         0.250         0.547
##  WPUBT_1        0.918         0.994         0.864         0.758         0.915
##  WPUBT_2        0.521         0.674         0.746         0.273         0.012
##  WPUBT_3        0.377         0.870         0.590         0.353         0.334
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.992         0.000
##  WPUBT_1        0.311         0.030         0.000
##  WPUBT_2        0.001         0.189         0.000         0.000
##  WPUBT_3        0.504         0.346         0.030         0.000         0.000
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\black full model.dgm
## 
##      Beginning Time:  11:58:49
##         Ending Time:  11:58:49
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen

White Youth Model (No Covariates)

# Specify the path to your Mplus output file
output_path <- "C:/Users/ocrobert/OneDrive - Indiana University/ABCD/Obesity Week/Mplus/white full model.out"

# Read and print the file
output_content <- readLines(output_path)
cat(output_content, sep = "\n")

## Mplus VERSION 8.10
## MUTHEN & MUTHEN
## 07/02/2024  12:01 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Full Sample Model
##   DATA: FILE = "Fullsample_race3_sex_subset.dat";
##   VARIABLE:
##   NAMES = sex race3 age_B int_B intt_B age_1 int_1 intt_1
##        age_2 int_2 intt_2 age_3 int_3 intt_3 wchr_B wchrt_B
##        wchr_1 wchrt_1 wchr_2 wchrt_2 wchr_3 wchrt_3 pub_B pubt_B
##        pub_1 pubt_1 pub_2 pubt_2 pub_3 pubt_3 int_p_ave famc_ave bw_lbs matage
##        matalc_ave matcig_ave matmar_ave ses_lt;
##   MISSING=.;
## 
##   USEVARIABLES ARE
##   wchrt_b wchrt_1
##   wchrt_2 wchrt_3
##   intt_b intt_1
##   intt_2 intt_3
##   pubt_b pubt_1
##   pubt_2 pubt_3;
## 
##   USEOBSERVATIONS ARE (race3 EQ 1);
## 
##   DEFINE:
##   wchrt_b = wchrt_b*10;
##   wchrt_1 = wchrt_1*10;
##   wchrt_2 = wchrt_2*10;
##   wchrt_3 = wchrt_3*10;
## 
##   ANALYSIS:
##   ESTIMATOR=MLR;
##   MODEL=NOCOVARIANCES;
##   COVERAGE = 0;
## 
##   MODEL:
##   ! Estimate random inttercept)
##   RI_intt BY intt_b@1 intt_1@1 intt_2@1 intt_3@1;
##   RI_pubtT BY pubt_b@1 pubt_1@1 pubt_2@1 pubt_3@1;
##   RI_wchrt BY wchrt_b@1 wchrt_1@1 wchrt_2@1 wchrt_3@1;
## 
##   ! RI correlations
##   RI_intt with RI_pubtT RI_wchrt;
##   RI_pubtT with RI_wchrt;
## 
##   ! Create within-person centered variables
##   wintt_b BY intt_b@1;
##   wintt_1 BY intt_1@1;
##   wintt_2 BY intt_2@1;
##   wintt_3 BY intt_3@1;
## 
##   wwchrt_b BY wchrt_b@1;
##   wwchrt_1 BY wchrt_1@1;
##   wwchrt_2 BY wchrt_2@1;
##   wwchrt_3 BY wchrt_3@1;
## 
##   wpubt_b BY pubt_b@1;
##   wpubt_1 BY pubt_1@1;
##   wpubt_2 BY pubt_2@1;
##   wpubt_3 BY pubt_3@1;
## 
##   ! Constrain the measurement error variances to zero
##   intt_b@0;
##   intt_1@0;
##   intt_2@0;
##   intt_3@0;
## 
##   wchrt_b@0;
##   wchrt_1@0;
##   wchrt_2@0;
##   wchrt_3@0;
## 
##   pubt_b@0;
##   pubt_1@0;
##   pubt_2@0;
##   pubt_3@0;
## 
##   ! Estimate the Lagged Effects
##   wwchrt_1 ON wwchrt_b;
##   wwchrt_1 ON wintt_b;
##   wwchrt_1 ON wpubt_b;
## 
##   wwchrt_2 ON wwchrt_1;
##   wwchrt_2 ON wintt_1;
##   wwchrt_2 ON wpubt_1;
## 
##   wwchrt_3 ON wwchrt_2;
##   wwchrt_3 ON wintt_2;
##   wwchrt_3 ON wpubt_2;
## 
##   wpubt_1 ON wpubt_b;
##   wpubt_1 ON wintt_b;
##   wpubt_1 ON wwchrt_b;
## 
##   wpubt_2 ON wpubt_1;
##   wpubt_2 ON wintt_1;
##   wpubt_2 ON wwchrt_1;
## 
##   wpubt_3 ON wpubt_2;
##   wpubt_3 ON wintt_2;
##   wpubt_3 ON wwchrt_2;
## 
##   wintt_1 ON wintt_b;
##   wintt_1 ON wpubt_b;
##   wintt_1 ON wwchrt_b;
## 
##   wintt_2 ON wintt_1;
##   wintt_2 ON wpubt_1;
##   wintt_2 ON wwchrt_1;
## 
##   wintt_3 ON wintt_2;
##   wintt_3 ON wpubt_2;
##   wintt_3 ON wwchrt_2;
## 
##   ! Estimate the covariance between the within-person
##   ! centered variables at the first wave
##   wintt_b with wpubt_b;
##   wwchrt_b with wintt_b wpubt_b;
## 
##   ! Estimate covariances between residuals of within-person components
##   ! (i.e., innovations)
##   wintt_1 with wpubt_1 wwchrt_1;
##   wpubt_1 with wwchrt_1;
## 
##   wintt_2 with wpubt_2 wwchrt_2;
##   wpubt_2 with wwchrt_2;
## 
##   wintt_3 with wpubt_3 wwchrt_3;
##   wpubt_3 with wwchrt_3;
## 
##   ! ask for variances for all variables that are included;
##   [intt_b intt_1 intt_2 intt_3];
##   [pubt_b pubt_1 pubt_2 pubt_3];
##   [wchrt_b wchrt_1 wchrt_2 wchrt_3];
## 
##   ! Fix the correlation between the individual factors and the other
##   ! exogenous variables to zero (by default these would be estimated)
##   RI_wchrt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_intt with wwchrt_b@0 wintt_b@0 wpubt_b@0;
##   RI_pubtT with wwchrt_b@0 wintt_b@0 wpubt_b@0;
## 
##   OUTPUT: STDYX MODINDICES Tech4;
## 
## 
## 
## *** WARNING
##   Data set contains cases with missing on all variables.
##   These cases were not included in the analysis.
##   Number of cases with missing on all variables:  1
##    1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
## 
## 
## 
## Full Sample Model
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                        6171
## 
## Number of dependent variables                                   12
## Number of independent variables                                  0
## Number of continuous latent variables                           15
## 
## Observed dependent variables
## 
##   Continuous
##    WCHRT_B     WCHRT_1     WCHRT_2     WCHRT_3     INTT_B      INTT_1
##    INTT_2      INTT_3      PUBT_B      PUBT_1      PUBT_2      PUBT_3
## 
## Continuous latent variables
##    RI_INTT     RI_PUBTT    RI_WCHRT    WINTT_B     WINTT_1     WINTT_2
##    WINTT_3     WWCHRT_B    WWCHRT_1    WWCHRT_2    WWCHRT_3    WPUBT_B
##    WPUBT_1     WPUBT_2     WPUBT_3
## 
## 
## Estimator                                                      MLR
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Fullsample_race3_sex_subset.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns           162
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.000
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               WCHRT_B       WCHRT_1       WCHRT_2       WCHRT_3       INTT_B
##               ________      ________      ________      ________      ________
##  WCHRT_B        0.998
##  WCHRT_1        0.961         0.963
##  WCHRT_2        0.812         0.803         0.813
##  WCHRT_3        0.180         0.178         0.166         0.181
##  INTT_B         0.998         0.962         0.813         0.180         0.999
##  INTT_1         0.966         0.962         0.805         0.179         0.968
##  INTT_2         0.943         0.928         0.812         0.179         0.944
##  INTT_3         0.887         0.873         0.770         0.180         0.888
##  PUBT_B         0.825         0.796         0.682         0.162         0.825
##  PUBT_1         0.468         0.465         0.450         0.118         0.468
##  PUBT_2         0.910         0.898         0.784         0.171         0.911
##  PUBT_3         0.875         0.860         0.759         0.175         0.876
## 
## 
##            Covariance Coverage
##               INTT_1        INTT_2        INTT_3        PUBT_B        PUBT_1
##               ________      ________      ________      ________      ________
##  INTT_1         0.968
##  INTT_2         0.933         0.945
##  INTT_3         0.878         0.877         0.889
##  PUBT_B         0.800         0.781         0.739         0.826
##  PUBT_1         0.468         0.457         0.447         0.427         0.468
##  PUBT_2         0.901         0.907         0.847         0.760         0.446
##  PUBT_3         0.865         0.862         0.861         0.732         0.444
## 
## 
##            Covariance Coverage
##               PUBT_2        PUBT_3
##               ________      ________
##  PUBT_2         0.912
##  PUBT_3         0.843         0.877
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      WCHRT_B              -0.146       1.105      -1.812    0.02%      -0.603     -0.366     -0.252
##             6160.000       0.340       2.034       3.298    0.02%      -0.123      0.256
##      WCHRT_1              -0.132       2.805      -2.125    0.02%      -0.620     -0.386     -0.261
##             5941.000       0.447      26.088       9.378    0.02%      -0.126      0.290
##      WCHRT_2              -0.139       1.519      -2.197    0.02%      -0.667     -0.413     -0.279
##             5017.000       0.453       8.055       9.026    0.02%      -0.131      0.350
##      WCHRT_3              -0.153       2.126      -1.493    0.09%      -0.707     -0.448     -0.301
##             1114.000       0.523      13.217       7.699    0.09%      -0.173      0.343
##      INTT_B               -0.064       2.525      -1.161    0.26%      -1.096     -0.936     -0.917
##             6167.000       2.584       8.608      12.919    0.02%      -0.143      0.882
##      INTT_1               -0.047       2.446      -1.281    0.03%      -1.132     -1.059     -0.993
##             5974.000       2.962       7.519      12.912    0.02%      -0.154      0.883
##      INTT_2               -0.026       2.345      -1.697    0.02%      -1.281     -1.119     -1.030
##             5829.000       3.659       6.956      13.867    0.02%      -0.293      0.861
##      INTT_3                0.012       2.098      -1.822    0.04%      -1.453     -1.296     -0.630
##             5484.000       4.589       5.261      13.693    0.02%      -0.394      1.397
##      PUBT_B               -0.108       0.148      -1.606    0.14%      -0.943     -0.151      0.045
##             5096.000       0.597      -0.731       3.039    0.02%       0.061      0.622
##      PUBT_1               -0.097      -0.002      -2.124    0.07%      -0.903     -0.084     -0.009
##             2888.000       0.602      -0.378       3.082    0.03%       0.112      0.552
##      PUBT_2               -0.128      -0.269      -2.839    0.02%      -0.768     -0.266     -0.112
##             5627.000       0.557       0.055       2.854    0.02%       0.079      0.531
##      PUBT_3               -0.088      -0.381      -2.940    0.02%      -0.693     -0.238      0.032
##             5409.000       0.545       0.286       2.154    0.02%       0.170      0.496
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       69
## 
## Loglikelihood
## 
##           H0 Value                      -76379.100
##           H0 Scaling Correction Factor      2.6729
##             for MLR
##           H1 Value                      -76301.931
##           H1 Scaling Correction Factor      2.3340
##             for MLR
## 
## Information Criteria
## 
##           Akaike (AIC)                  152896.200
##           Bayesian (BIC)                153360.406
##           Sample-Size Adjusted BIC      153141.142
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                            126.438*
##           Degrees of Freedom                    21
##           P-Value                           0.0000
##           Scaling Correction Factor         1.2207
##             for MLR
## 
## *   The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
##     for chi-square difference testing in the regular way.  MLM, MLR and WLSM
##     chi-square difference testing is described on the Mplus website.  MLMV, WLSMV,
##     and ULSMV difference testing is done using the DIFFTEST option.
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.029
##           90 Percent C.I.                    0.024  0.033
##           Probability RMSEA <= .05           1.000
## 
## CFI/TLI
## 
##           CFI                                0.989
##           TLI                                0.965
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                           9451.286
##           Degrees of Freedom                    66
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.016
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             1.000      0.000    999.000    999.000
##     INTT_1             1.000      0.000    999.000    999.000
##     INTT_2             1.000      0.000    999.000    999.000
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  RI_PUBTT BY
##     PUBT_B             1.000      0.000    999.000    999.000
##     PUBT_1             1.000      0.000    999.000    999.000
##     PUBT_2             1.000      0.000    999.000    999.000
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  RI_WCHRT BY
##     WCHRT_B            1.000      0.000    999.000    999.000
##     WCHRT_1            1.000      0.000    999.000    999.000
##     WCHRT_2            1.000      0.000    999.000    999.000
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WINTT_B  BY
##     INTT_B             1.000      0.000    999.000    999.000
## 
##  WINTT_1  BY
##     INTT_1             1.000      0.000    999.000    999.000
## 
##  WINTT_2  BY
##     INTT_2             1.000      0.000    999.000    999.000
## 
##  WINTT_3  BY
##     INTT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_B BY
##     WCHRT_B            1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            1.000      0.000    999.000    999.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            1.000      0.000    999.000    999.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            1.000      0.000    999.000    999.000
## 
##  WPUBT_B  BY
##     PUBT_B             1.000      0.000    999.000    999.000
## 
##  WPUBT_1  BY
##     PUBT_1             1.000      0.000    999.000    999.000
## 
##  WPUBT_2  BY
##     PUBT_2             1.000      0.000    999.000    999.000
## 
##  WPUBT_3  BY
##     PUBT_3             1.000      0.000    999.000    999.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.102      0.080     -1.269      0.204
##     WINTT_B           -0.032      0.018     -1.715      0.086
##     WPUBT_B           -0.012      0.016     -0.782      0.434
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.219      0.045      4.882      0.000
##     WINTT_1            0.030      0.011      2.630      0.009
##     WPUBT_1            0.022      0.020      1.088      0.276
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.535      0.108      4.974      0.000
##     WINTT_2            0.022      0.012      1.799      0.072
##     WPUBT_2           -0.003      0.025     -0.118      0.906
## 
##  WPUBT_1  ON
##     WPUBT_B            0.230      0.029      7.967      0.000
##     WINTT_B            0.008      0.027      0.306      0.760
##     WWCHRT_B          -0.041      0.118     -0.344      0.731
## 
##  WPUBT_2  ON
##     WPUBT_1            0.357      0.024     14.763      0.000
##     WINTT_1           -0.006      0.012     -0.484      0.628
##     WWCHRT_1          -0.030      0.025     -1.204      0.228
## 
##  WPUBT_3  ON
##     WPUBT_2            0.427      0.019     22.612      0.000
##     WINTT_2            0.018      0.008      2.334      0.020
##     WWCHRT_2          -0.023      0.022     -1.016      0.310
## 
##  WINTT_1  ON
##     WINTT_B           -0.041      0.072     -0.562      0.574
##     WPUBT_B           -0.024      0.040     -0.603      0.546
##     WWCHRT_B           0.014      0.188      0.076      0.939
## 
##  WINTT_2  ON
##     WINTT_1            0.229      0.048      4.747      0.000
##     WPUBT_1            0.134      0.050      2.682      0.007
##     WWCHRT_1           0.014      0.053      0.258      0.796
## 
##  WINTT_3  ON
##     WINTT_2            0.465      0.032     14.602      0.000
##     WPUBT_2            0.116      0.037      3.151      0.002
##     WWCHRT_2           0.204      0.069      2.950      0.003
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.033      0.016      2.132      0.033
##     RI_WCHRT           0.126      0.015      8.453      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.056      0.006      9.810      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B           -0.007      0.017     -0.387      0.699
##     WWCHRT_B          -0.019      0.011     -1.773      0.076
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B           -0.008      0.006     -1.372      0.170
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1            0.005      0.026      0.210      0.834
##     WWCHRT_1          -0.002      0.018     -0.119      0.905
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.001      0.011      0.044      0.965
## 
##  WINTT_2  WITH
##     WPUBT_2            0.016      0.014      1.148      0.251
##     WWCHRT_2           0.031      0.011      2.820      0.005
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.005      0.005     -1.102      0.271
## 
##  WINTT_3  WITH
##     WPUBT_3            0.051      0.013      3.938      0.000
##     WWCHRT_3           0.028      0.027      1.026      0.305
## 
##  WPUBT_3  WITH
##     WWCHRT_3          -0.012      0.009     -1.353      0.176
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B           -0.145      0.007    -19.545      0.000
##     WCHRT_1           -0.129      0.009    -14.982      0.000
##     WCHRT_2           -0.134      0.009    -14.683      0.000
##     WCHRT_3           -0.228      0.015    -15.409      0.000
##     INTT_B            -0.063      0.020     -3.075      0.002
##     INTT_1            -0.037      0.022     -1.677      0.093
##     INTT_2            -0.017      0.025     -0.669      0.503
##     INTT_3             0.038      0.029      1.315      0.188
##     PUBT_B            -0.109      0.011    -10.132      0.000
##     PUBT_1            -0.085      0.013     -6.358      0.000
##     PUBT_2            -0.125      0.010    -12.659      0.000
##     PUBT_3            -0.087      0.010     -8.756      0.000
## 
##  Variances
##     RI_INTT            1.796      0.089     20.086      0.000
##     RI_PUBTT           0.101      0.011      9.384      0.000
##     RI_WCHRT           0.260      0.009     29.043      0.000
##     WINTT_B            0.867      0.073     11.925      0.000
##     WWCHRT_B           0.081      0.006     13.258      0.000
##     WPUBT_B            0.501      0.013     37.525      0.000
## 
##  Residual Variances
##     WCHRT_B            0.000      0.000    999.000    999.000
##     WCHRT_1            0.000      0.000    999.000    999.000
##     WCHRT_2            0.000      0.000    999.000    999.000
##     WCHRT_3            0.000      0.000    999.000    999.000
##     INTT_B             0.000      0.000    999.000    999.000
##     INTT_1             0.000      0.000    999.000    999.000
##     INTT_2             0.000      0.000    999.000    999.000
##     INTT_3             0.000      0.000    999.000    999.000
##     PUBT_B             0.000      0.000    999.000    999.000
##     PUBT_1             0.000      0.000    999.000    999.000
##     PUBT_2             0.000      0.000    999.000    999.000
##     PUBT_3             0.000      0.000    999.000    999.000
##     WINTT_1            1.092      0.096     11.348      0.000
##     WINTT_2            1.860      0.085     21.801      0.000
##     WINTT_3            2.407      0.100     24.141      0.000
##     WWCHRT_1           0.184      0.030      6.075      0.000
##     WWCHRT_2           0.189      0.019      9.836      0.000
##     WWCHRT_3           0.199      0.036      5.541      0.000
##     WPUBT_1            0.462      0.015     31.516      0.000
##     WPUBT_2            0.392      0.010     40.924      0.000
##     WPUBT_3            0.361      0.009     40.688      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.272E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
## STANDARDIZED MODEL RESULTS
## 
## 
## STDYX Standardization
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  RI_INTT  BY
##     INTT_B             0.821      0.013     61.885      0.000
##     INTT_1             0.788      0.016     48.148      0.000
##     INTT_2             0.695      0.012     57.447      0.000
##     INTT_3             0.622      0.013     47.914      0.000
## 
##  RI_PUBTT BY
##     PUBT_B             0.410      0.022     18.963      0.000
##     PUBT_1             0.414      0.023     17.860      0.000
##     PUBT_2             0.427      0.023     18.703      0.000
##     PUBT_3             0.431      0.023     18.975      0.000
## 
##  RI_WCHRT BY
##     WCHRT_B            0.874      0.010     90.127      0.000
##     WCHRT_1            0.764      0.027     28.501      0.000
##     WCHRT_2            0.753      0.018     40.964      0.000
##     WCHRT_3            0.709      0.040     17.699      0.000
## 
##  WINTT_B  BY
##     INTT_B             0.571      0.019     29.872      0.000
## 
##  WINTT_1  BY
##     INTT_1             0.615      0.021     29.311      0.000
## 
##  WINTT_2  BY
##     INTT_2             0.719      0.012     61.605      0.000
## 
##  WINTT_3  BY
##     INTT_3             0.783      0.010     75.991      0.000
## 
##  WWCHRT_B BY
##     WCHRT_B            0.487      0.017     27.954      0.000
## 
##  WWCHRT_1 BY
##     WCHRT_1            0.645      0.032     20.349      0.000
## 
##  WWCHRT_2 BY
##     WCHRT_2            0.658      0.021     31.320      0.000
## 
##  WWCHRT_3 BY
##     WCHRT_3            0.705      0.040     17.536      0.000
## 
##  WPUBT_B  BY
##     PUBT_B             0.912      0.010     93.811      0.000
## 
##  WPUBT_1  BY
##     PUBT_1             0.910      0.011     86.201      0.000
## 
##  WPUBT_2  BY
##     PUBT_2             0.904      0.011     84.012      0.000
## 
##  WPUBT_3  BY
##     PUBT_3             0.903      0.011     83.385      0.000
## 
##  WWCHRT_1 ON
##     WWCHRT_B          -0.067      0.052     -1.284      0.199
##     WINTT_B           -0.068      0.041     -1.678      0.093
##     WPUBT_B           -0.020      0.025     -0.792      0.428
## 
##  WWCHRT_2 ON
##     WWCHRT_1           0.212      0.038      5.607      0.000
##     WINTT_1            0.070      0.027      2.549      0.011
##     WPUBT_1            0.034      0.032      1.070      0.284
## 
##  WWCHRT_3 ON
##     WWCHRT_2           0.470      0.057      8.311      0.000
##     WINTT_2            0.059      0.036      1.659      0.097
##     WPUBT_2           -0.004      0.034     -0.117      0.907
## 
##  WPUBT_1  ON
##     WPUBT_B            0.232      0.028      8.313      0.000
##     WINTT_B            0.011      0.036      0.306      0.760
##     WWCHRT_B          -0.016      0.048     -0.344      0.731
## 
##  WPUBT_2  ON
##     WPUBT_1            0.370      0.025     14.882      0.000
##     WINTT_1           -0.009      0.019     -0.485      0.628
##     WWCHRT_1          -0.019      0.016     -1.211      0.226
## 
##  WPUBT_3  ON
##     WPUBT_2            0.431      0.018     23.924      0.000
##     WINTT_2            0.037      0.016      2.333      0.020
##     WWCHRT_2          -0.015      0.015     -1.025      0.306
## 
##  WINTT_1  ON
##     WINTT_B           -0.036      0.065     -0.560      0.575
##     WPUBT_B           -0.016      0.027     -0.602      0.547
##     WWCHRT_B           0.004      0.051      0.076      0.939
## 
##  WINTT_2  ON
##     WINTT_1            0.172      0.038      4.480      0.000
##     WPUBT_1            0.068      0.025      2.696      0.007
##     WWCHRT_1           0.004      0.016      0.259      0.796
## 
##  WINTT_3  ON
##     WINTT_2            0.382      0.025     15.364      0.000
##     WPUBT_2            0.046      0.015      3.163      0.002
##     WWCHRT_2           0.054      0.018      3.073      0.002
## 
##  RI_INTT  WITH
##     RI_PUBTT           0.078      0.036      2.153      0.031
##     RI_WCHRT           0.184      0.020      9.156      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  RI_PUBTT WITH
##     RI_WCHRT           0.344      0.038      8.963      0.000
##     WWCHRT_B           0.000      0.000    999.000    999.000
##     WINTT_B            0.000      0.000    999.000    999.000
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  WINTT_B  WITH
##     WPUBT_B           -0.010      0.026     -0.387      0.699
##     WWCHRT_B          -0.073      0.042     -1.730      0.084
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WWCHRT_B WITH
##     WPUBT_B           -0.042      0.031     -1.368      0.171
##     RI_WCHRT           0.000      0.000    999.000    999.000
## 
##  WINTT_1  WITH
##     WPUBT_1            0.008      0.036      0.210      0.834
##     WWCHRT_1          -0.005      0.039     -0.119      0.905
## 
##  WPUBT_1  WITH
##     WWCHRT_1           0.002      0.039      0.044      0.965
## 
##  WINTT_2  WITH
##     WPUBT_2            0.019      0.016      1.153      0.249
##     WWCHRT_2           0.051      0.019      2.782      0.005
## 
##  WPUBT_2  WITH
##     WWCHRT_2          -0.019      0.017     -1.109      0.267
## 
##  WINTT_3  WITH
##     WPUBT_3            0.055      0.014      3.969      0.000
##     WWCHRT_3           0.040      0.040      0.987      0.324
## 
##  WPUBT_3  WITH
##     WWCHRT_3          -0.044      0.034     -1.323      0.186
## 
##  RI_WCHRT WITH
##     WPUBT_B            0.000      0.000    999.000    999.000
## 
##  Intercepts
##     WCHRT_B           -0.249      0.015    -16.888      0.000
##     WCHRT_1           -0.194      0.017    -11.173      0.000
##     WCHRT_2           -0.198      0.016    -12.322      0.000
##     WCHRT_3           -0.317      0.031    -10.100      0.000
##     INTT_B            -0.039      0.013     -2.926      0.003
##     INTT_1            -0.022      0.013     -1.636      0.102
##     INTT_2            -0.009      0.013     -0.663      0.507
##     INTT_3             0.018      0.013      1.338      0.181
##     PUBT_B            -0.140      0.014     -9.991      0.000
##     PUBT_1            -0.111      0.017     -6.332      0.000
##     PUBT_2            -0.168      0.013    -12.859      0.000
##     PUBT_3            -0.118      0.013     -8.921      0.000
## 
##  Variances
##     RI_INTT            1.000      0.000    999.000    999.000
##     RI_PUBTT           1.000      0.000    999.000    999.000
##     RI_WCHRT           1.000      0.000    999.000    999.000
##     WINTT_B            1.000      0.000    999.000    999.000
##     WWCHRT_B           1.000      0.000    999.000    999.000
##     WPUBT_B            1.000      0.000    999.000    999.000
## 
##  Residual Variances
##     WCHRT_B            0.000    999.000    999.000    999.000
##     WCHRT_1            0.000    999.000    999.000    999.000
##     WCHRT_2            0.000    999.000    999.000    999.000
##     WCHRT_3            0.000    999.000    999.000    999.000
##     INTT_B             0.000    999.000    999.000    999.000
##     INTT_1             0.000    999.000    999.000    999.000
##     INTT_2             0.000    999.000    999.000    999.000
##     INTT_3             0.000    999.000    999.000    999.000
##     PUBT_B             0.000    999.000    999.000    999.000
##     PUBT_1             0.000    999.000    999.000    999.000
##     PUBT_2             0.000    999.000    999.000    999.000
##     PUBT_3             0.000    999.000    999.000    999.000
##     WINTT_1            0.998      0.005    214.255      0.000
##     WINTT_2            0.966      0.014     69.614      0.000
##     WINTT_3            0.845      0.020     43.081      0.000
##     WWCHRT_1           0.991      0.009    109.704      0.000
##     WWCHRT_2           0.949      0.017     56.631      0.000
##     WWCHRT_3           0.772      0.051     14.985      0.000
##     WPUBT_1            0.945      0.013     73.921      0.000
##     WPUBT_2            0.863      0.018     47.162      0.000
##     WPUBT_3            0.811      0.016     52.004      0.000
## 
## 
## R-SQUARE
## 
##     Observed                                        Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WCHRT_B            1.000    999.000    999.000    999.000
##     WCHRT_1            1.000    999.000    999.000    999.000
##     WCHRT_2            1.000    999.000    999.000    999.000
##     WCHRT_3            1.000    999.000    999.000    999.000
##     INTT_B             1.000    999.000    999.000    999.000
##     INTT_1             1.000    999.000    999.000    999.000
##     INTT_2             1.000    999.000    999.000    999.000
##     INTT_3             1.000    999.000    999.000    999.000
##     PUBT_B             1.000    999.000    999.000    999.000
##     PUBT_1             1.000    999.000    999.000    999.000
##     PUBT_2             1.000    999.000    999.000    999.000
##     PUBT_3             1.000    999.000    999.000    999.000
## 
##      Latent                                         Two-Tailed
##     Variable        Estimate       S.E.  Est./S.E.    P-Value
## 
##     WINTT_1            0.002      0.005      0.345      0.730
##     WINTT_2            0.034      0.014      2.475      0.013
##     WINTT_3            0.155      0.020      7.920      0.000
##     WWCHRT_1           0.009      0.009      0.971      0.331
##     WWCHRT_2           0.051      0.017      3.033      0.002
##     WWCHRT_3           0.228      0.051      4.433      0.000
##     WPUBT_1            0.055      0.013      4.281      0.000
##     WPUBT_2            0.137      0.018      7.495      0.000
##     WPUBT_3            0.189      0.016     12.117      0.000
## 
## 
## MODEL MODIFICATION INDICES
## 
## NOTE:  Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included.  To include these, request
## MODINDICES (ALL).
## 
## Minimum M.I. value for printing the modification index    10.000
## 
##                                    M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
## 
## BY Statements
## 
## RI_INTT  BY INTT_B                67.214    -0.325     -0.435       -0.267
## RI_INTT  BY INTT_1                59.436     0.251      0.337        0.198
## RI_PUBTT BY PUBT_1                10.715     0.375      0.119        0.155
## WINTT_B  BY INTT_3                39.992    -0.231     -0.215       -0.100
## WINTT_1  BY INTT_2                60.744    -0.502     -0.525       -0.272
## WINTT_1  BY INTT_3                62.316     0.238      0.249        0.115
## WINTT_3  BY INTT_B                49.904    -0.105     -0.177       -0.109
## WINTT_3  BY INTT_1                62.045     0.107      0.180        0.106
## WINTT_3  BY INTT_2                63.225    -0.797     -1.346       -0.697
## WWCHRT_B BY WCHRT_3               12.226    -0.298     -0.085       -0.118
## WWCHRT_3 BY WCHRT_B               11.256    -0.140     -0.071       -0.122
## WWCHRT_3 BY WCHRT_2               10.774    -0.551     -0.280       -0.413
## WPUBT_B  BY PUBT_3                12.299    -0.074     -0.052       -0.071
## WPUBT_1  BY PUBT_2                20.170    -0.251     -0.175       -0.235
## WPUBT_1  BY PUBT_3                19.290     0.105      0.074        0.100
## WPUBT_3  BY PUBT_B                21.260    -0.158     -0.105       -0.135
## WPUBT_3  BY PUBT_1                22.039     0.115      0.077        0.100
## WPUBT_3  BY PUBT_2                19.920    -0.325     -0.217       -0.291
## 
## ON/BY Statements
## 
## RI_INTT  ON WINTT_B  /
## WINTT_B  BY RI_INTT               64.800    -0.616     -0.428       -0.428
## RI_INTT  ON WINTT_1  /
## WINTT_1  BY RI_INTT               62.087     0.440      0.343        0.343
## RI_PUBTT ON WPUBT_B  /
## WPUBT_B  BY RI_PUBTT              17.494    -0.256     -0.569       -0.569
## RI_PUBTT ON WPUBT_1  /
## WPUBT_1  BY RI_PUBTT              18.329     0.178      0.392        0.392
## WINTT_B  ON RI_INTT  /
## RI_INTT  BY WINTT_B               67.118    -0.309     -0.445       -0.445
## WINTT_B  ON WINTT_3  /
## WINTT_3  BY WINTT_B               51.136    -0.102     -0.185       -0.185
## WINTT_1  ON RI_INTT  /
## RI_INTT  BY WINTT_1               62.994     0.288      0.369        0.369
## WINTT_1  ON WINTT_3  /
## WINTT_3  BY WINTT_1               61.751     0.110      0.178        0.178
## WINTT_2  ON WINTT_3  /
## WINTT_3  BY WINTT_2               63.270    -0.798     -0.970       -0.970
## WINTT_3  ON WINTT_B  /
## WINTT_B  BY WINTT_3               39.992    -0.231     -0.128       -0.128
## WINTT_3  ON WINTT_1  /
## WINTT_1  BY WINTT_3               62.316     0.238      0.147        0.147
## WWCHRT_B ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_B              11.593    -0.131     -0.235       -0.235
## WWCHRT_2 ON WWCHRT_3 /
## WWCHRT_3 BY WWCHRT_2              10.775    -0.551     -0.627       -0.627
## WWCHRT_3 ON WWCHRT_B /
## WWCHRT_B BY WWCHRT_3              12.226    -0.298     -0.167       -0.167
## WPUBT_B  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_B               16.116    -0.170     -0.160       -0.160
## WPUBT_1  ON RI_PUBTT /
## RI_PUBTT BY WPUBT_1               20.826     0.706      0.321        0.321
## WPUBT_1  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_1               22.388     0.132      0.126        0.126
## WPUBT_2  ON WPUBT_3  /
## WPUBT_3  BY WPUBT_2               19.908    -0.325     -0.321       -0.321
## WPUBT_3  ON WPUBT_B  /
## WPUBT_B  BY WPUBT_3               12.299    -0.074     -0.078       -0.078
## WPUBT_3  ON WPUBT_1  /
## WPUBT_1  BY WPUBT_3               19.290     0.105      0.110        0.110
## 
## WITH Statements
## 
## WCHRT_3  WITH WCHRT_B             12.462    -0.026     -0.026      999.000
## INTT_2   WITH WCHRT_2             11.752     0.362      0.362      999.000
## INTT_2   WITH INTT_1              60.026    -0.533     -0.533      999.000
## INTT_3   WITH INTT_B              37.300    -0.200     -0.200      999.000
## INTT_3   WITH INTT_1              62.628     0.257      0.257      999.000
## INTT_3   WITH INTT_2              62.692    -1.909     -1.909      999.000
## PUBT_2   WITH PUBT_1              28.894    -0.111     -0.111      999.000
## PUBT_3   WITH PUBT_B              17.764    -0.040     -0.040      999.000
## PUBT_3   WITH PUBT_1              24.132     0.044      0.044      999.000
## PUBT_3   WITH PUBT_2              19.844    -0.117     -0.117      999.000
## WINTT_B  WITH RI_INTT             62.504    -0.526     -0.421       -0.421
## WINTT_1  WITH RI_INTT             62.880     0.498      0.356        0.356
## WINTT_3  WITH WINTT_B             39.145    -0.199     -0.138       -0.138
## WINTT_3  WITH WINTT_1             62.370     0.266      0.164        0.164
## WINTT_3  WITH WINTT_2             62.716    -1.910     -0.903       -0.903
## WWCHRT_3 WITH WWCHRT_B            13.033    -0.025     -0.198       -0.198
## WPUBT_B  WITH RI_PUBTT            16.917    -0.126     -0.558       -0.558
## WPUBT_1  WITH RI_PUBTT            18.551     0.072      0.332        0.332
## WPUBT_3  WITH WPUBT_B             12.140    -0.037     -0.086       -0.086
## WPUBT_3  WITH WPUBT_1             24.779     0.051      0.126        0.126
## WPUBT_3  WITH WPUBT_2             19.833    -0.117     -0.311       -0.311
## 
## Variances/Residual Variances
## 
## WCHRT_2                           12.950     0.220      0.220        0.480
## INTT_2                            63.421     4.114      4.114        1.105
## PUBT_2                            20.397     0.277      0.277        0.498
## 
## 
## TECHNICAL 4 OUTPUT
## 
## 
##      ESTIMATES DERIVED FROM THE MODEL
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 0.000         0.000         0.000         0.000         0.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##                 1.000         1.000         1.000         1.000         1.000
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.796
##  RI_PUBTT       0.033         0.101
##  RI_WCHRT       0.126         0.056         0.260
##  WINTT_B        0.000         0.000         0.000         0.867
##  WINTT_1        0.000         0.000         0.000        -0.035         1.094
##  WINTT_2        0.000         0.000         0.000        -0.008         0.250
##  WINTT_3        0.000         0.000         0.000        -0.004         0.122
##  WWCHRT_B       0.000         0.000         0.000        -0.019         0.002
##  WWCHRT_1       0.000         0.000         0.000        -0.025        -0.001
##  WWCHRT_2       0.000         0.000         0.000        -0.006         0.032
##  WWCHRT_3       0.000         0.000         0.000        -0.004         0.023
##  WPUBT_B        0.000         0.000         0.000        -0.007        -0.012
##  WPUBT_1        0.000         0.000         0.000         0.007         0.002
##  WPUBT_2        0.000         0.000         0.000         0.003        -0.006
##  WPUBT_3        0.000         0.000         0.000         0.001         0.001
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.926
##  WINTT_3        0.908         2.849
##  WWCHRT_B       0.000        -0.001         0.081
##  WWCHRT_1       0.002         0.009        -0.007         0.186
##  WWCHRT_2       0.040         0.059        -0.002         0.041         0.199
##  WWCHRT_3       0.063         0.079        -0.001         0.022         0.107
##  WPUBT_B        0.013         0.011        -0.008        -0.005         0.001
##  WPUBT_1        0.066         0.053        -0.005        -0.001         0.011
##  WPUBT_2        0.038         0.070        -0.002        -0.006        -0.003
##  WPUBT_3        0.049         0.096        -0.001        -0.003        -0.005
## 
## 
##            ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.258
##  WPUBT_B        0.001         0.501
##  WPUBT_1        0.007         0.115         0.489
##  WPUBT_2       -0.002         0.041         0.174         0.455
##  WPUBT_3       -0.014         0.018         0.075         0.195         0.445
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.089
##  RI_PUBTT       0.016         0.011
##  RI_WCHRT       0.015         0.006         0.009
##  WINTT_B        0.000         0.000         0.000         0.073
##  WINTT_1        0.000         0.000         0.000         0.060         0.093
##  WINTT_2        0.000         0.000         0.000         0.014         0.066
##  WINTT_3        0.000         0.000         0.000         0.008         0.036
##  WWCHRT_B       0.000         0.000         0.000         0.011         0.014
##  WWCHRT_1       0.000         0.000         0.000         0.015         0.016
##  WWCHRT_2       0.000         0.000         0.000         0.004         0.015
##  WWCHRT_3       0.000         0.000         0.000         0.003         0.009
##  WPUBT_B        0.000         0.000         0.000         0.017         0.019
##  WPUBT_1        0.000         0.000         0.000         0.025         0.027
##  WPUBT_2        0.000         0.000         0.000         0.009         0.017
##  WPUBT_3        0.000         0.000         0.000         0.004         0.008
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.097
##  WINTT_3        0.086         0.134
##  WWCHRT_B       0.004         0.002         0.006
##  WWCHRT_1       0.011         0.007         0.006         0.030
##  WWCHRT_2       0.013         0.016         0.001         0.009         0.020
##  WWCHRT_3       0.024         0.030         0.001         0.007         0.026
##  WPUBT_B        0.009         0.005         0.006         0.007         0.003
##  WPUBT_1        0.028         0.017         0.010         0.011         0.012
##  WPUBT_2        0.018         0.021         0.004         0.006         0.007
##  WPUBT_3        0.018         0.019         0.002         0.003         0.006
## 
## 
##            S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.058
##  WPUBT_B        0.002         0.013
##  WPUBT_1        0.008         0.016         0.018
##  WPUBT_2        0.012         0.007         0.016         0.015
##  WPUBT_3        0.011         0.004         0.009         0.013         0.014
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT       20.086
##  RI_PUBTT       2.132         9.384
##  RI_WCHRT       8.453         9.810        29.043
##  WINTT_B        0.000         0.000         0.000        11.925
##  WINTT_1        0.000         0.000         0.000        -0.589        11.777
##  WINTT_2        0.000         0.000         0.000        -0.532         3.787
##  WINTT_3        0.000         0.000         0.000        -0.593         3.382
##  WWCHRT_B       0.000         0.000         0.000        -1.773         0.149
##  WWCHRT_1       0.000         0.000         0.000        -1.727        -0.067
##  WWCHRT_2       0.000         0.000         0.000        -1.478         2.105
##  WWCHRT_3       0.000         0.000         0.000        -1.366         2.406
##  WPUBT_B        0.000         0.000         0.000        -0.387        -0.618
##  WPUBT_1        0.000         0.000         0.000         0.261         0.085
##  WPUBT_2        0.000         0.000         0.000         0.372        -0.333
##  WPUBT_3        0.000         0.000         0.000         0.369         0.157
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2       19.945
##  WINTT_3       10.502        21.187
##  WWCHRT_B      -0.090        -0.339        13.258
##  WWCHRT_1       0.193         1.285        -1.257         6.199
##  WWCHRT_2       3.095         3.741        -1.214         4.653         9.878
##  WWCHRT_3       2.646         2.610        -1.145         3.072         4.139
##  WPUBT_B        1.448         2.084        -1.372        -0.687         0.309
##  WPUBT_1        2.321         3.105        -0.537        -0.051         0.907
##  WPUBT_2        2.087         3.277        -0.481        -0.971        -0.406
##  WPUBT_3        2.781         5.058        -0.455        -1.174        -0.884
## 
## 
##            EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       4.469
##  WPUBT_B        0.317        37.525
##  WPUBT_1        0.781         7.207        26.432
##  WPUBT_2       -0.161         5.541        10.931        31.282
##  WPUBT_3       -1.312         4.841         8.330        15.300        31.129
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.033         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.556         0.000
##  WINTT_2        1.000         1.000         1.000         0.595         0.000
##  WINTT_3        1.000         1.000         1.000         0.553         0.001
##  WWCHRT_B       1.000         1.000         1.000         0.076         0.882
##  WWCHRT_1       1.000         1.000         1.000         0.084         0.947
##  WWCHRT_2       1.000         1.000         1.000         0.139         0.035
##  WWCHRT_3       1.000         1.000         1.000         0.172         0.016
##  WPUBT_B        1.000         1.000         1.000         0.699         0.537
##  WPUBT_1        1.000         1.000         1.000         0.794         0.932
##  WPUBT_2        1.000         1.000         1.000         0.710         0.739
##  WPUBT_3        1.000         1.000         1.000         0.712         0.875
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.929         0.734         0.000
##  WWCHRT_1       0.847         0.199         0.209         0.000
##  WWCHRT_2       0.002         0.000         0.225         0.000         0.000
##  WWCHRT_3       0.008         0.009         0.252         0.002         0.000
##  WPUBT_B        0.148         0.037         0.170         0.492         0.758
##  WPUBT_1        0.020         0.002         0.591         0.959         0.364
##  WPUBT_2        0.037         0.001         0.630         0.331         0.685
##  WPUBT_3        0.005         0.000         0.649         0.240         0.377
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.751         0.000
##  WPUBT_1        0.435         0.000         0.000
##  WPUBT_2        0.872         0.000         0.000         0.000
##  WPUBT_3        0.190         0.000         0.000         0.000         0.000
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        1.000
##  RI_PUBTT       0.078         1.000
##  RI_WCHRT       0.184         0.344         1.000
##  WINTT_B        0.000         0.000         0.000         1.000
##  WINTT_1        0.000         0.000         0.000        -0.036         1.000
##  WINTT_2        0.000         0.000         0.000        -0.006         0.172
##  WINTT_3        0.000         0.000         0.000        -0.003         0.069
##  WWCHRT_B       0.000         0.000         0.000        -0.073         0.007
##  WWCHRT_1       0.000         0.000         0.000        -0.063        -0.002
##  WWCHRT_2       0.000         0.000         0.000        -0.016         0.069
##  WWCHRT_3       0.000         0.000         0.000        -0.008         0.043
##  WPUBT_B        0.000         0.000         0.000        -0.010        -0.016
##  WPUBT_1        0.000         0.000         0.000         0.010         0.003
##  WPUBT_2        0.000         0.000         0.000         0.005        -0.008
##  WPUBT_3        0.000         0.000         0.000         0.002         0.002
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        1.000
##  WINTT_3        0.388         1.000
##  WWCHRT_B      -0.001        -0.001         1.000
##  WWCHRT_1       0.004         0.012        -0.061         1.000
##  WWCHRT_2       0.064         0.078        -0.013         0.212         1.000
##  WWCHRT_3       0.089         0.092        -0.006         0.100         0.474
##  WPUBT_B        0.013         0.009        -0.042        -0.017         0.003
##  WPUBT_1        0.068         0.045        -0.027        -0.002         0.034
##  WPUBT_2        0.041         0.061        -0.009        -0.020        -0.009
##  WPUBT_3        0.053         0.085        -0.004        -0.012        -0.017
## 
## 
##            ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       1.000
##  WPUBT_B        0.002         1.000
##  WPUBT_1        0.019         0.233         1.000
##  WPUBT_2       -0.006         0.087         0.370         1.000
##  WPUBT_3       -0.042         0.038         0.161         0.433         1.000
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.036         0.000
##  RI_WCHRT       0.020         0.038         0.000
##  WINTT_B        0.000         0.000         0.000         0.000
##  WINTT_1        0.000         0.000         0.000         0.064         0.000
##  WINTT_2        0.000         0.000         0.000         0.011         0.039
##  WINTT_3        0.000         0.000         0.000         0.005         0.018
##  WWCHRT_B       0.000         0.000         0.000         0.042         0.049
##  WWCHRT_1       0.000         0.000         0.000         0.038         0.035
##  WWCHRT_2       0.000         0.000         0.000         0.011         0.033
##  WWCHRT_3       0.000         0.000         0.000         0.006         0.017
##  WPUBT_B        0.000         0.000         0.000         0.026         0.026
##  WPUBT_1        0.000         0.000         0.000         0.038         0.037
##  WPUBT_2        0.000         0.000         0.000         0.014         0.024
##  WPUBT_3        0.000         0.000         0.000         0.006         0.011
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.025         0.000
##  WWCHRT_B       0.009         0.004         0.000
##  WWCHRT_1       0.019         0.009         0.051         0.000
##  WWCHRT_2       0.021         0.021         0.012         0.038         0.000
##  WWCHRT_3       0.036         0.039         0.006         0.023         0.056
##  WPUBT_B        0.009         0.004         0.031         0.024         0.011
##  WPUBT_1        0.029         0.014         0.051         0.037         0.038
##  WPUBT_2        0.019         0.018         0.019         0.020         0.022
##  WPUBT_3        0.019         0.017         0.008         0.010         0.019
## 
## 
##            S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.006         0.000
##  WPUBT_1        0.023         0.028         0.000
##  WPUBT_2        0.036         0.014         0.025         0.000
##  WPUBT_3        0.033         0.007         0.015         0.018         0.000
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT      999.000
##  RI_PUBTT       2.153       999.000
##  RI_WCHRT       9.156         8.963       999.000
##  WINTT_B        0.000         0.000         0.000       999.000
##  WINTT_1        0.000         0.000         0.000        -0.572       999.000
##  WINTT_2        0.000         0.000         0.000        -0.526         4.472
##  WINTT_3        0.000         0.000         0.000        -0.586         3.874
##  WWCHRT_B       0.000         0.000         0.000        -1.730         0.149
##  WWCHRT_1       0.000         0.000         0.000        -1.655        -0.067
##  WWCHRT_2       0.000         0.000         0.000        -1.457         2.135
##  WWCHRT_3       0.000         0.000         0.000        -1.389         2.550
##  WPUBT_B        0.000         0.000         0.000        -0.387        -0.616
##  WPUBT_1        0.000         0.000         0.000         0.261         0.085
##  WPUBT_2        0.000         0.000         0.000         0.372        -0.333
##  WPUBT_3        0.000         0.000         0.000         0.370         0.157
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2      999.000
##  WINTT_3       15.481       999.000
##  WWCHRT_B      -0.090        -0.338       999.000
##  WWCHRT_1       0.193         1.293        -1.201       999.000
##  WWCHRT_2       3.049         3.652        -1.164         5.524       999.000
##  WWCHRT_3       2.454         2.339        -1.128         4.252         8.531
##  WPUBT_B        1.458         2.114        -1.368        -0.695         0.308
##  WPUBT_1        2.352         3.184        -0.536        -0.051         0.901
##  WPUBT_2        2.111         3.321        -0.481        -0.976        -0.407
##  WPUBT_3        2.815         5.158        -0.455        -1.186        -0.886
## 
## 
##            EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3     999.000
##  WPUBT_B        0.320       999.000
##  WPUBT_1        0.804         8.455       999.000
##  WPUBT_2       -0.160         6.203        14.955       999.000
##  WPUBT_3       -1.260         5.323        10.430        24.062       999.000
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               RI_INTT       RI_PUBTT      RI_WCHRT      WINTT_B       WINTT_1
##               ________      ________      ________      ________      ________
##  RI_INTT        0.000
##  RI_PUBTT       0.031         0.000
##  RI_WCHRT       0.000         0.000         0.000
##  WINTT_B        1.000         1.000         1.000         0.000
##  WINTT_1        1.000         1.000         1.000         0.567         0.000
##  WINTT_2        1.000         1.000         1.000         0.599         0.000
##  WINTT_3        1.000         1.000         1.000         0.558         0.000
##  WWCHRT_B       1.000         1.000         1.000         0.084         0.882
##  WWCHRT_1       1.000         1.000         1.000         0.098         0.947
##  WWCHRT_2       1.000         1.000         1.000         0.145         0.033
##  WWCHRT_3       1.000         1.000         1.000         0.165         0.011
##  WPUBT_B        1.000         1.000         1.000         0.699         0.538
##  WPUBT_1        1.000         1.000         1.000         0.794         0.932
##  WPUBT_2        1.000         1.000         1.000         0.710         0.739
##  WPUBT_3        1.000         1.000         1.000         0.712         0.875
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WINTT_2       WINTT_3       WWCHRT_B      WWCHRT_1      WWCHRT_2
##               ________      ________      ________      ________      ________
##  WINTT_2        0.000
##  WINTT_3        0.000         0.000
##  WWCHRT_B       0.929         0.735         0.000
##  WWCHRT_1       0.847         0.196         0.230         0.000
##  WWCHRT_2       0.002         0.000         0.245         0.000         0.000
##  WWCHRT_3       0.014         0.019         0.260         0.000         0.000
##  WPUBT_B        0.145         0.035         0.171         0.487         0.758
##  WPUBT_1        0.019         0.001         0.592         0.959         0.368
##  WPUBT_2        0.035         0.001         0.631         0.329         0.684
##  WPUBT_3        0.005         0.000         0.649         0.235         0.376
## 
## 
##            TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
##               WWCHRT_3      WPUBT_B       WPUBT_1       WPUBT_2       WPUBT_3
##               ________      ________      ________      ________      ________
##  WWCHRT_3       0.000
##  WPUBT_B        0.749         0.000
##  WPUBT_1        0.421         0.000         0.000
##  WPUBT_2        0.873         0.000         0.000         0.000
##  WPUBT_3        0.208         0.000         0.000         0.000         0.000
## 
## 
## DIAGRAM INFORMATION
## 
##   Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
##   If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
## 
##   Diagram output
##     c:\users\ocrobert\onedrive - indiana university\abcd\obesity week\mplus\white full model.dgm
## 
##      Beginning Time:  12:01:54
##         Ending Time:  12:01:55
##        Elapsed Time:  00:00:01
## 
## 
## 
## MUTHEN & MUTHEN
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## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2023 Muthen & Muthen